// Numbas version: exam_results_page_options
{"name": "Integration by substitution 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"description": "<p>Integration by susbtitution, no hint given</p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "functions": {}, "tags": [], "variables": {"b": {"description": "", "definition": "random(1..8 except a)", "name": "b", "templateType": "anything", "group": "Ungrouped variables"}, "a": {"description": "", "definition": "random(2..6)", "name": "a", "templateType": "anything", "group": "Ungrouped variables"}, "c": {"description": "", "definition": "random(1..9)", "name": "c", "templateType": "anything", "group": "Ungrouped variables"}}, "name": "Integration by substitution 2", "parts": [{"prompt": "<p>$\\int e^x\\sqrt{1+e^x}\\mathrm{dx}$</p>", "checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "type": "jme", "showCorrectAnswer": true, "answer": "2(1+e^x)^(3/2)/3+C", "scripts": {}, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "checkvariablenames": false, "expectedvariablenames": [], "showFeedbackIcon": true}, {"prompt": "<p>$\\int\\frac{\\mathrm{dx}}{\\var{a}x+\\var{b}}$.</p>\n<p>Answer in terms of the natural log, represented by ln( ).</p>", "checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "type": "jme", "showCorrectAnswer": true, "answer": "1/{a}ln({a}x+{b})+C", "scripts": {}, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "checkvariablenames": false, "expectedvariablenames": [], "showFeedbackIcon": true}, {"prompt": "<p>$\\int \\frac{x \\mathrm{dx}}{\\var{c}+x^2}$.</p>\n<p>Answer in terms of the natural log, represented by ln( ).</p>", "checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "type": "jme", "showCorrectAnswer": true, "answer": "ln({c}+x^2)/2+C", "scripts": {}, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "checkvariablenames": false, "expectedvariablenames": [], "showFeedbackIcon": true}], "variable_groups": [], "ungrouped_variables": ["c", "b", "a"], "advice": "<p>integration by Susbtitution</p>", "statement": "<p>Evaluate the following indefinite integrals using integration by substitution. Use the letter C to represent any unknown constants.</p>", "type": "question", "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}]}]}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}]}