// Numbas version: exam_results_page_options {"name": "Integrate powers of $x$", "metadata": {"description": "

Quiz designed to test integration of powers of x including negative powers, surds, fractions, etc.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": "80", "showQuestionGroupNames": true, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Basic", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Integrate powers of $x$ (basic)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "

Positive whole powers only

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\\]

", "advice": "

By basic integration:

\\[\\simplify[fractionNumbers,all]{{a/(b+1)}*x^{b+1}+{c/(d+1)}*x^{d+1}+{f/(g+1)}*x^{g+1}+c}\\]

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You forgot the constant of integration.

", "useAlternativeFeedback": false, "answer": "{a/(b+1)}*x^{b+1}+{c/(d+1)}*x^{d+1}+{f/(g+1)}*x^{g+1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a/(b+1)}*x^{b+1}+{c/(d+1)}*x^{d+1}+{f/(g+1)}*x^{g+1}+c", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Integrate powers of $x$ (basic)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "

Positive whole powers only

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\\]

", "advice": "

By basic integration:

\\[\\simplify[fractionNumbers,all]{{a/(b+1)}*x^{b+1}+{c/(d+1)}*x^{d+1}+{f/(g+1)}*x^{g+1}+c}\\]

You forgot the constant of integration.

Positive whole powers only

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\\]

", "advice": "

By basic integration:

\\[\\simplify[fractionNumbers,all]{{a/(b+1)}*x^{b+1}+{c/(d+1)}*x^{d+1}+{f/(g+1)}*x^{g+1}+c}\\]

You forgot the constant of integration.

Positive whole powers only

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\\]

", "advice": "

By basic integration:

\\[\\simplify[fractionNumbers,all]{{a/(b+1)}*x^{b+1}+{c/(d+1)}*x^{d+1}+{f/(g+1)}*x^{g+1}+c}\\]

You forgot the constant of integration.

", "useAlternativeFeedback": false, "answer": "{a/(b+1)}*x^{b+1}+{c/(d+1)}*x^{d+1}+{f/(g+1)}*x^{g+1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a/(b+1)}*x^{b+1}+{c/(d+1)}*x^{d+1}+{f/(g+1)}*x^{g+1}+c", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "With decimals and negatives", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Integrate powers of $x$ (negative and decimal)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "

Powers including some decimals and negatives

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}}\\;dx\\]

", "advice": "

Using basic integration:

\\[\\simplify[fractionNumbers,all]{{a/(b+1)}*x^{b+1}+{1/(c*(d+1))}*x^{d+1}+{f}*x+c}\\]

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You forgot the constant of integration!

", "useAlternativeFeedback": false, "answer": "{a}/{b+1}*x^{b+1}+1/{c*(d+1)}*x^{d+1}+{f}*x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a}/{b+1}*x^{b+1}+1/{c*(d+1)}*x^{d+1}+{f}*x+c", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Integrate powers of $x$ (negative and decimal)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "

Powers including some decimals and negatives

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}}\\;dx\\]

", "advice": "

Using basic integration:

\\[\\simplify[fractionNumbers,all]{{a/(b+1)}*x^{b+1}+{1/(c*(d+1))}*x^{d+1}+{f}*x+c}\\]

You forgot the constant of integration!

Powers including some decimals and negatives

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}}\\;dx\\]

", "advice": "

Using basic integration:

\\[\\simplify[fractionNumbers,all]{{a/(b+1)}*x^{b+1}+{1/(c*(d+1))}*x^{d+1}+{f}*x+c}\\]

You forgot the constant of integration!

Powers including some decimals and negatives

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}}\\;dx\\]

", "advice": "

Using basic integration:

\\[\\simplify[fractionNumbers,all]{{a/(b+1)}*x^{b+1}+{1/(c*(d+1))}*x^{d+1}+{f}*x+c}\\]

You forgot the constant of integration!

", "useAlternativeFeedback": false, "answer": "{a}/{b+1}*x^{b+1}+1/{c*(d+1)}*x^{d+1}+{f}*x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a}/{b+1}*x^{b+1}+1/{c*(d+1)}*x^{d+1}+{f}*x+c", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "$x$ in the denominator", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Integrate powers of $x$ (reciprocals)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "

Including powers of x in the denominator

", "licence": "None specified"}, "statement": "

You will integrate the following function:

\\[\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\\]

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"g": {"name": "g", "group": "Ungrouped variables", "definition": "random(1..5 except [b,d])", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(1..10 except[b,c])", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..10 except a)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(0..3 #0.1 except [b,1])", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f", "a", "b", "c", "d", "g"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

First rewrite the integral without any fractions.

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

Any terms without fractions can be left unchanged.

$\\int$ [[0]]$dx$

", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "jme", "useCustomName": true, "customName": "Premature integration", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "

Do not integrate any of the terms yet.

", "useAlternativeFeedback": false, "answer": "{a}*x^{-b}+{c}*x^{-d}+{f/(g+1)}*x^{g+1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a}*x^{-b}+{c}*x^{-d}+{f}*x^{g}", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Now integrate.

", "alternatives": [{"type": "jme", "useCustomName": true, "customName": "No constant", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "

You forgot the constant of integration!

", "useAlternativeFeedback": false, "answer": "{a}/{-b+1}*x^{-b+1}+{c}/{-d+1}*x^{-d+1}+{f}/{g+1}*x^{g+1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a}/{-b+1}*x^{-b+1}+{c}/{-d+1}*x^{-d+1}+{f}/{g+1}*x^{g+1}+c", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Integrate powers of $x$ (reciprocals)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "

Including powers of x in the denominator

", "licence": "None specified"}, "statement": "

You will integrate the following function:

\\[\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\\]

First rewrite the integral without any fractions.

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

Any terms without fractions can be left unchanged.

$\\int$ [[0]]$dx$

Do not integrate any of the terms yet.

Now integrate.

You forgot the constant of integration!

Including powers of x in the denominator

", "licence": "None specified"}, "statement": "

You will integrate the following function:

\\[\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\\]

First rewrite the integral without any fractions.

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

Any terms without fractions can be left unchanged.

$\\int$ [[0]]$dx$

Do not integrate any of the terms yet.

Now integrate.

You forgot the constant of integration!

Including powers of x in the denominator

", "licence": "None specified"}, "statement": "

You will integrate the following function:

\\[\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\\]

First rewrite the integral without any fractions.

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

Any terms without fractions can be left unchanged.

$\\int$ [[0]]$dx$

Do not integrate any of the terms yet.

Now integrate.

You forgot the constant of integration!

", "useAlternativeFeedback": false, "answer": "{a}/{-b+1}*x^{-b+1}+{c}/{-d+1}*x^{-d+1}+{f}/{g+1}*x^{g+1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a}/{-b+1}*x^{-b+1}+{c}/{-d+1}*x^{-d+1}+{f}/{g+1}*x^{g+1}+c", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Surds", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Integrate powers of $x$ (surds)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "

Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*sqrt(x)-{c}*root(x,{n})+{f}*x^{g}}\\;dx\\]

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(1..10 except [a,c])", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..10 except a)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(3..6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f", "a", "c", "g", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

First rewrite the integral using powers of $x$ only.

Remember that:

$\\sqrt{x}=x^\\frac{1}{2}$;
$\\sqrt[3]{x}=x^\\frac{1}{3}$; etc.

Any terms without roots can be left unchanged.

$\\int$ [[0]]$dx$

Do not integrate any of the terms yet.

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Now integrate.

You forgot the constant of integration!

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Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*sqrt(x)-{c}*root(x,{n})+{f}*x^{g}}\\;dx\\]

First rewrite the integral using powers of $x$ only.

Remember that:

$\\sqrt{x}=x^\\frac{1}{2}$;
$\\sqrt[3]{x}=x^\\frac{1}{3}$; etc.

Any terms without roots can be left unchanged.

$\\int$ [[0]]$dx$

Do not integrate any of the terms yet.

Now integrate.

You forgot the constant of integration!

Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*sqrt(x)-{c}*root(x,{n})+{f}*x^{g}}\\;dx\\]

First rewrite the integral using powers of $x$ only.

Remember that:

$\\sqrt{x}=x^\\frac{1}{2}$;
$\\sqrt[3]{x}=x^\\frac{1}{3}$; etc.

Any terms without roots can be left unchanged.

$\\int$ [[0]]$dx$

Do not integrate any of the terms yet.

Now integrate.

You forgot the constant of integration!

Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "statement": "

Integrate the following:

\\[\\int\\simplify{{a}*sqrt(x)-{c}*root(x,{n})+{f}*x^{g}}\\;dx\\]

First rewrite the integral using powers of $x$ only.

Remember that:

$\\sqrt{x}=x^\\frac{1}{2}$;
$\\sqrt[3]{x}=x^\\frac{1}{3}$; etc.

Any terms without roots can be left unchanged.

$\\int$ [[0]]$dx$

Do not integrate any of the terms yet.

Now integrate.

You forgot the constant of integration!

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Including powers of x in the denominator

", "licence": "None specified"}, "statement": "

This is a challenging question designed to test all the different skills you have learned.

Integrate the following:

\\[\\int\\simplify{{a}/({b}*x^{d})-{c}/sqrt(x)+{b}*root(x,3)/{f}+{g}*x}\\;dx\\]

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First rewrite the integral using powers of $x$.

$\\int$ [[0]]$dx$

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Now integrate.

You forgot the constant of integration!

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You have 5 minutes left!

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