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Question: If \(\int_{}^{}\frac{1}{(1 + x)\sqrt{x}}\)dx = f (x) + A, where A is any arbitrary constant, then th...

If ∫1(1+x)x\int_{}^{}\frac{1}{(1 + x)\sqrt{x}}dx = f (x) + A, where A is any arbitrary constant, then the function f (x) is –

A

2 tan–1x

B

2 tan–1x\sqrt{x}

C

2 cot–1x\sqrt{x}

D

loge (1 + x)

Answer

2 tan–1x\sqrt{x}

Explanation

Solution

Put x\sqrt { \mathrm { x } } = t

= dtdx\frac { \mathrm { dt } } { \mathrm { dx } } ̃ = 2dt

= 2 tan–1t + C