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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1
If ∫02dxx+1+(x+1)3\int\limits_{0}^2 \frac{d x}{\sqrt{x+1}+\sqrt{(x+1)^3}} is equal to kπk \pi then kk is equal to
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Correct option: C
16\frac{1}{6}
Option C (16\frac{1}{6}) is correct because the integral can be simplified by substitution, leading to an arctangent integral which evaluates to the given value.

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