{"@context":"https://schema.org/","@type":"Quiz","dateCreated":"2026-04-24T08:12:25.319Z","dateModified":"2026-04-24T08:12:25.319Z","typicalAgeRange":"11-18","educationalLevel":"KCET","assesses":"Mathematics - integral","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalTopic","targetName":"integral"},{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"Mathematics"},{"@type":"AlignmentObject","alignmentType":"educationalExam","targetName":"KCET"}],"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":"$$ \\int \\frac{1}{(x-3)(x-7)} \\, dx = ? $$}","encodingFormat":"text/markdown","comment":{"@type":"Comment","text":"Always subtract the smaller constant from the larger constant ($7 - 3$) to determine the coefficient in front of the logarithm."},"suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

$\\frac{1}{4} \\log \\left( \\frac{x+7}{x+3} \\right) + c$

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

$\\frac{1}{4} \\log \\left( \\frac{x-7}{x+3} \\right) + c$

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

$\\frac{1}{4} \\log \\left( \\frac{x-7}{x-3} \\right) + c$

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

None\n\n

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

$\\frac{1}{4} \\log \\left( \\frac{x-7}{x-3} \\right) + c$

","comment":{"@type":"Comment","text":"Always subtract the smaller constant from the larger constant ($7 - 3$) to determine the coefficient in front of the logarithm."},"answerExplanation":{"@type":"comment","text":""}}}]}

$$ \int \frac{1}{(x-3)(x-7)} \, dx = ? $$

Show Hint

The Correct Option is C

Solution and Explanation

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