If ∫log⁡$$x+1+x21+x2dx=gof$$⁡$$(x)+$$ constant, then

Correct option is 3f(x)=log⁡x+x2+1 and g(x)=x22

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If $\int \frac{\log (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} dx = gof (x) +$ constant, 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)=x22

f(x)=x22 and g(x)=log⁡x+x2+1

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detailed solution

Correct option is C

On putting log⁡x+1+x2=t⇒1x+1+x2×1+x1+x2dx=dt⇒ dx1+x2=dt∴ ∫log⁡x+1+x21+x2dx=∫tdt=12t2+C=12log⁡x+x2+12+C

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If ∫log⁡x+1+x21+x2dx=gof⁡(x)+ constant, then

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If $\int \frac{\log (x + \sqrt{1 + x^{2}})}{\sqrt{1 + x^{2}}} dx = gof (x) +$ constant, then