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If $\int_{0}^{2} \frac{d x}{\sqrt{x + 1} + \sqrt{(x + 1)^{3}}}$ is equal to $k π$ then $k$ is equal to

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detailed solution

Correct option is C

The given integral in equal to∫02 dxx+1(2+x)=∫13 2tdttt2+1,t2=x+1 =2∫13 dtt2+1=2tan−1⁡t13=2π3−π4=π6.

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If ∫02 dxx+1+(x+1)3 is equal to kπ then k is equal to

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If $\int_{0}^{2} \frac{d x}{\sqrt{x + 1} + \sqrt{(x + 1)^{3}}}$ is equal to $k π$ then $k$ is equal to