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The following questions may be useful if you wish to have some extra practice. Your names are not being recorded

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Question was not attempted

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Simple Indefinite Integrals

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Solve the following indefinite integrals, using $C$ to represent an unknown constant.

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Indefinite Integrals

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$\\int(x^4-\\var{a}x^3+\\var{b}x-\\var{c})\\mathrm{dx}$

", "answer": "x^5/5-{a}x^4/4+{b}x^2/2-{c}x+C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

$\\int(u+\\var{d})(2u+\\var{f})\\mathrm{du}$

", "answer": "2u^3/3+u^2({f}+2{d})/2+{d}{f}u+C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "u", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

$\\int\\frac{\\sin(2x)}{\\sin(x)}\\mathrm{dx}$.

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Take care to include the brackets in the trigonometric expressions, i.e. write sin(x) rather than sinx.

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$\\int (\\frac{2}{x^4}+\\frac{3}{x}+1)\\mathrm{dx}$

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$\\int(q^3+\\sqrt{q})\\mathrm{dq}$

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$\\int(x^2-6+\\frac{x}{2})\\mathrm{dx}$

", "answer": "x^3/3-6x+x^2/4+C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

$\\int{(\\frac{3}{4}-2p+\\frac{4}{p^2}})\\mathrm{dp}$

", "answer": "3/4p-p^2-4/p+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "p", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

$\\int{(\\frac{1}{4}\\sqrt{x}-3\\sqrt{x^5})}\\mathrm{dx}$

", "answer": "1/6x^(3/2)-6/7x^(7/2)+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}]}]}], "showstudentname": false, "duration": 0, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "type": "exam", "contributors": [{"name": "George Dobre", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3230/"}], "extensions": [], "custom_part_types": [], "resources": []}