{"@context":"https://schema.org/","@type":"Quiz","dateCreated":"2025-01-22T12:07:57.756Z","dateModified":"2025-11-26T04:29:21.150Z","typicalAgeRange":"11-18","educationalLevel":"MHT CET","assesses":"Mathematics - integral","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalTopic","targetName":"integral"},{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"Mathematics"},{"@type":"AlignmentObject","alignmentType":"educationalExam","targetName":"MHT CET"}],"name":"Quiz about integral","about":{"@type":"Thing","name":"Mathematics - integral"},"hasPart":[{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"intermediate","name":"Question About integral","text":"The value of : $$ \\int \\frac{x + 1}{x(1 + xe^x)} dx $$.}","encodingFormat":"text/markdown","comment":{"@type":"Comment","text":"When solving logarithmic integrals, identify substitutions that transform the integrand into simpler rational expressions."},"suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

\$ \\log \\left| \\frac{1 + xe^x} {xe^x} \\right| + C \$\n

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":1,"encodingFormat":"text/markdown","text":"

\$ \\log \\left| \\frac{xe^x}{1 + xe^x} \\right| + C \$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":2,"encodingFormat":"text/markdown","text":"

\$ \\log \\left| xe^x(1 + xe^x) \\right| + C \$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":3,"encodingFormat":"text/markdown","text":"

\$ \\log \\left| 1 + xe^x \\right| + C \$

","comment":{"@type":"Comment","text":"\"\""}}],"acceptedAnswer":{"@type":"Answer","position":1,"encodingFormat":"text/markdown","text":"

\$ \\log \\left| \\frac{xe^x}{1 + xe^x} \\right| + C \$

","comment":{"@type":"Comment","text":"When solving logarithmic integrals, identify substitutions that transform the integrand into simpler rational expressions."},"answerExplanation":{"@type":"comment","text":""}}}]}

The value of : \( \int \frac{x + 1}{x(1 + xe^x)} dx \).

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