JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

The value of

\int \frac{1}{x+\sqrt{x-1}} d x

, is

View answer and explanation

Correct option: C

\log (x+\sqrt{x-1})-\frac{2}{3} \tan ^{-1}\left(\frac{2 \sqrt{x-1}+1}{\sqrt{3}}\right)+C

Option C,

\log (x+\sqrt{x-1})-\frac{2}{3} \tan ^{-1}\left(\frac{2 \sqrt{x-1}+1}{\sqrt{3}}\right)+C

, is correct because using the substitution

x-1=t^2

and completing the square leads to this result.

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