// Numbas version: exam_results_page_options {"name": "Indefinite Integrals Q8 2019 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"showfrontpage": false, "preventleave": false, "allowregen": true}, "question_groups": [{"questions": [{"variable_groups": [], "name": "Indefinite Integrals Q8 2019 (custom feedback)", "variables": {"d": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "d", "definition": "random(1..8)"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a", "definition": "random(2..9)"}, "f": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "f", "definition": "random(1..8 except d)"}, "b": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b", "definition": "random(2..9 except a)"}, "c": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "c", "definition": "random(1..9 except a except b)"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Simple Indefinite Integrals

\n

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Indefinite Integrals

", "ungrouped_variables": ["a", "c", "b", "d", "f"], "extensions": [], "rulesets": {}, "functions": {}, "parts": [{"checkVariableNames": false, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "malrules:\n [\n [\"1/6x^(3/2)-6/7x^(7/2)\",\"Don't forget the constant of integration!\"],\n [\"1/6x^(3/2)-2(x^5)^(3/2)+C\", \"Check the second term again. Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/6x^(3/2)-2(x^5)^(3/2)\", \"Check the second term again. Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/4x^(1/2)-2(x^5)^(3/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/4x^(1/2)-2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/4x^(1/2)-9/2(x^5)^(3/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/4x^(1/2)-9/2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/4x^(1/2)-6/7x^(7/2)\", \"You need to look at the first term again. $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated.\"],\n [\"1/4x^(1/2)-6/7x^(7/2)+C\", \"You need to look at the first term again. $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated.\"],\n [\"1/4x^(1/2)-21/2x^(7/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\"],\n [\"1/4x^(1/2)-21/2x^(7/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\"],\n [\"1/2x^(1/2)-2(x^5)^(3/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/2x^(1/2)-2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/2x^(1/2)-9/2(x^5)^(3/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/2x^(1/2)-9/2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"1/2x^(1/2)-6/7x^(7/2)\", \"You need to look at the first term again. $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated.\"],\n [\"1/2x^(1/2)-6/7x^(7/2)+C\", \"You need to look at the first term again. $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated.\"],\n [\"1/2x^(1/2)-21/2x^(7/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\"],\n [\"1/2x^(1/2)-21/2x^(7/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\"],\n [\"3/8x^(3/2)-2(x^5)^(3/2)\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"3/8x^(3/2)-2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"3/8x^(3/2)-9/2(x^5)^(3/2)\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"3/8x^(3/2)-9/2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\"],\n [\"3/8x^(3/2)-6/7x^(7/2)\", \"You need to look at the first term again. It looks like you have multiplied by the new power of $\\\\frac{3}{2}$.\"],\n [\"3/8x^(3/2)-6/7x^(7/2)+C\", \"You need to look at the first term again. It looks like you have multiplied by the new power of $\\\\frac{3}{2}$.\"],\n [\"3/8x^(3/2)-21/2x^(7/2)\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\"],\n [\"3/8x^(3/2)-21/2x^(7/2)+C\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\"],\n [\"1/6x^(3/2)-21/2x^(7/2)\", \"You need to look at the second term again. It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\"],\n [\"1/6x^(3/2)-21/2x^(7/2)+C\", \"You need to look at the second term again. It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x),\"feedback\":x],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))$\\int{(\\frac{1}{4}\\sqrt{x}-3\\sqrt{x^5})}\\mathrm{dx}$

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

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