JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{\log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \mathrm{~d} x=g o f(x)+

Const. then

View answer and explanation

Correct option: C

f(x)=\log \left(x+\sqrt{x^2+1}\right)

and

g(x)=x^2 / 2

The correct answer is C (

f(x)=\log (x+\sqrt{x^2+1})

and

g(x)=x^2 / 2

) because after substituting

t = \log(x + \sqrt{1+x^2})

, the integral becomes

\int t dt = t^2/2 + C

, which matches the given form.

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