Indefinite Integrals

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

", "preamble": {"js": "", "css": ""}, "variables": {"b": {"definition": "random(2..9 except a)", "name": "b", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "f": {"definition": "random(1..8 except d)", "name": "f", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "a": {"definition": "random(2..9)", "name": "a", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "c": {"definition": "random(1..9 except a except b)", "name": "c", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "d": {"definition": "random(1..8)", "name": "d", "templateType": "anything", "description": "", "group": "Ungrouped variables"}}, "variable_groups": [], "ungrouped_variables": ["a", "c", "b", "d", "f"], "parts": [{"vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "failureRate": 1, "vsetRangePoints": 5, "unitTests": [], "prompt": "$\\int (\\frac{2}{x^4}+\\frac{3}{x}+1)\\mathrm{dx}$

", "variableReplacementStrategy": "originalfirst", "showPreview": true, "scripts": {}, "expectedVariableNames": [], "type": "jme", "marks": 1, "checkingType": "absdiff", "variableReplacements": [], "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n [\n [\"-2/3*1/x^3+3ln(x)+x\",\"Don't forget the constant of integration!\"], \n [\"-2x^(-5)/5+3ln(x)+x+C\", \"Check the first term again. It looks like you have subtracted 1 from the power.\"],\n [\"-2x^(-5)/5+3ln(x)+x\", \"Check the first term again. It looks like you have subtracted 1 from the power.\"],\n [\"-2x^(-5)/5+ln(3x)+x+C\", \"The first two terms are incorrect. First term: It looks like you have subtracted 1 from the power. 2nd term: $\\\\frac{3}{x}=3\\\\left(\\\\frac{1}{x}\\\\right)$. What do you get when you integrate $\\\\frac{1}{x}$?\"],\n [\"-2x^(-5)/5+ln(3x)+x\", \"The first two terms are incorrect. First term: It looks like you have subtracted 1 from the power. 2nd term: $\\\\frac{3}{x}=3\\\\left(\\\\frac{1}{x}\\\\right)$. What do you get when you integrate $\\\\frac{1}{x}$?\"],\n [\"-2/(3x^3)+ln(3x)+x+C\", \"Check the second term: $\\\\frac{3}{x}=3\\\\left(\\\\frac{1}{x}\\\\right)$. What do you get when you integrate $\\\\frac{1}{x}$?\"],\n [\"-2/(3x^3)+ln(3x)+x\", \"Check the second term: $\\\\frac{3}{x}=3\\\\left(\\\\frac{1}{x}\\\\right)$. What do you get when you integrate $\\\\frac{1}{x}$?\"],\n [\"-2/(3x^3)+3+x+C\", \"Check the second term: $\\\\frac{3}{x}=3x^{-1}$. The power rule doesn't work if the power on the $x$ is $-1$, because we would end up getting $\\\\frac{x^0}{0}$ and dividing by zero is not defined.\"],\n [\"-2/(3x^3)+3+x\", \"Check the second term: $\\\\frac{3}{x}=3x^{-1}$. The power rule doesn't work if the power on the $x$ is $-1$, because we would end up getting $\\\\frac{x^0}{0}$ and dividing by zero is not defined.\"],\n [\"-2x^(-5)/5+3+x+C\", \"The first two terms are incorrect. First term: It looks like you have subtracted 1 from the power. 2nd term: $\\\\frac{3}{x}=3x^{-1}$. The power rule doesn't work if the power on the $x$ is $-1$, because we would end up getting $\\\\frac{x^0}{0}$ and dividing by zero is not defined.\"],\n [\"-2x^(-5)/5+3+x\", \"The first two terms are incorrect. First term: It looks like you have subtracted 1 from the power. 2nd term: $\\\\frac{3}{x}=3x^{-1}$. The power rule doesn't work if the power on the $x$ is $-1$, because we would end up getting $\\\\frac{x^0}{0}$ and dividing by zero is not defined.\"],\n [\"2ln(x^4)+3ln(x)+x\",\"Check the first term again. You can only use the $\\\\ln$ rule if the power on the variable below the line is 1.\"],\n [\"2ln(x^4)+3ln(x)+x+C\",\"Check the first term again. You can only use the $\\\\ln$ rule if the power on the variable below the line is 1.\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x[0]),\"feedback\":x[1]],\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 )))