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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫cos⁡x(1+sin⁡x)(2+sin⁡x)dx=\int \frac{\cos x}{(1+\sin x)(2+\sin x)} d x=
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Correct option: C
log⁡1+sin⁡x2+sin⁡x+c\log \frac{1+\sin x}{2+\sin x}+c
Option C is correct because the integral is solved by substituting sin⁡x=t\sin x = t and using partial fraction decomposition.

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