Integration by susbtitution. Use the letter C for the constant.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Perform the following integration, using the letter $C$ to represent any unknown constants.
", "advice": "integration by Susbtitution
", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..20)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..8 except a)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["c", "b", "a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "malrules:\n [\n [\"(1/{c})*sin({c}x+2)\", \"Almost there! Did you forget to include the integration constant?\"],\n [\"-{c}*sin({c}x+2)+C\", \"It looks like you differentiated rather than integrating.\"],\n [\"-{c}*sin({c}x+2)\", \"It looks like you differentiated rather than integrating.\"],\n [\"-(1/{c})*sin({c}x+2)+C\", \"Double check the rule for integrating $\\\\cos(x)$.\"],\n [\"-(1/{c})*sin({c}x+2)\", \"Double check the rule for integrating $\\\\cos(x)$.\"],\n [\"{c}*sin({c}x+2)+C\", \"It looks like you have multiplied by the number in front of $x$. Did you mean to do this?\"],\n [\"{c}*sin({c}x+2)\", \"It looks like you have multiplied by the number in front of $x$. Did you mean to do this?\"],\n [\"sin({c}x+2)+C\",\"Did you forget to divide by the number in front of $x$?\"],\n [\"sin({c}x+2)\",\"Did you forget to divide by the number in front of $x$?\"]\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 )))