The value of the integral

Question:

The value of the integral $\int_{-1}^{1} \log \left(x+\sqrt{x^{2}+1}\right) d x$ is:

  1. 2

  2. 0

  3. -1

  4. 1


Correct Option: , 2

Solution:

Let $I=\int_{-1}^{1} \log \left(x+\sqrt{x^{2}+1}\right) d x$

$\because \log \left(x+\sqrt{x^{2}+1}\right)$ is an odd function

$\therefore I=0$

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