{"@context":"https://schema.org/","@type":"Quiz","dateCreated":"2026-03-24T11:20:21.207Z","dateModified":"2026-03-24T11:20:21.207Z","typicalAgeRange":"11-18","educationalLevel":"BITSAT","assesses":"Mathematics - Integration","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalTopic","targetName":"Integration"},{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"Mathematics"},{"@type":"AlignmentObject","alignmentType":"educationalExam","targetName":"BITSAT"}],"name":"Quiz about Integration","about":{"@type":"Thing","name":"Mathematics - Integration"},"hasPart":[{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"intermediate","name":"Question About Integration","text":"Evaluate:\n$$\n\\int \\frac{1}{1+3\\sin^2 x+8\\cos^2 x}\\,dx\n$$}","encodingFormat":"text/markdown","comment":{"@type":"Comment","text":"Convert trigonometric expressions using identities before substitution."},"suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

\$\\dfrac{1}{6}\\tan^{-1}(2\\tan x)+C\$

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

\$\\tan^{-1}(2\\tan x)+C\$

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

\$\\dfrac{1}{6}\\tan^{-1}\\!\\left(\\dfrac{2\\tan x}{3}\\right)+C\$

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

None of these\n\n

","comment":{"@type":"Comment","text":"\"\""}}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

\$\\dfrac{1}{6}\\tan^{-1}(2\\tan x)+C\$

","comment":{"@type":"Comment","text":"Convert trigonometric expressions using identities before substitution."},"answerExplanation":{"@type":"comment","text":""}}}]}

Evaluate: \[ \int \frac{1}{1+3\sin^2 x+8\cos^2 x}\,dx \]

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The Correct Option is A

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