If ∫log⁡$$x+1+x21+x2dx=g$$∘$$f(x)+Const$$. then

Correct option is 3f(x)=log⁡x+x2+1 and g(x)=x2/2

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If $\int \frac{\log (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} d x = g \circ f (x) +$
Const. then

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f(x)=log⁡x+x2+1

f(x)=log⁡x+x2+1 and g(x)=x2

f(x)=log⁡x+x2+1 and g(x)=x2/2

f(x)=x2/2 and g(x)=log⁡x+x2+1

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detailed solution

Correct option is C

Putting log⁡x+1+x2=t, we have1x+1+x2×1+x1+x2dx=dt i.e. dx1+x2=dtSo, ∫log⁡x+1+x21+x2dx=∫tdt=12t2+C=12log⁡x+x2+12+CThus f(x)=log⁡x+x2+1 and g(x)=x2/2.

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If ∫log⁡x+1+x21+x2dx=g∘f(x)+Const. then

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free study material

If $\int \frac{\log (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} d x = g \circ f (x) +$
Const. then