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If $f (x) = \sqrt{x}, g (x) = e^{x} - 1$ and $h (x) = \tan^{- 1} x$
then the anti derivative of $(f o g) (x)$ is

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2[(g∘f)(x)−(g∘f∘h)(x)]+C

2[(f∘g)(x)−(f∘g∘h)(x)]+C

(f∘g)(x)+(f∘g∘h)(x)+C

2[(f∘g)(x)−(h∘f∘g)(x)]+C

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detailed solution

Correct option is D

I=∫ex−1dxPut ex−1=t2, so that exdx=2tdt∴I=∫t2tt2+1dt=2∫t2+1−1t2+1dt=2t−tan−1⁡t+C=2ex−1−tan−1⁡ex−1+C=2[( fog )(x)−( hofog )(x)]+C.

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If f(x)=x,g(x)=ex−1 and h(x)=tan−1⁡x then the anti derivative of (f o g) (x) is

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If $f (x) = \sqrt{x}, g (x) = e^{x} - 1$ and $h (x) = \tan^{- 1} x$
then the anti derivative of $(f o g) (x)$ is