∫ log(x + √x^2 + 1) dx; x ∈ [-1, 2] =

Question

\(\int \limits_{-1}^2 \log(x+ \sqrt{x^2 + 1}) dx \)

(1) \(\log[(2 + \sqrt 5)^2 (\sqrt 2 - 1)] - \sqrt 5 + \sqrt 2\)

(2) \(\log[(2 + \sqrt 5)^2 (\sqrt 2 - 1)] + \sqrt 5 - \sqrt 2\)

(3) \(\log[(2 + \sqrt 5)^2 (\sqrt 2 - 1)] +\sqrt 5 + \sqrt 2\)

(4) \(\log(2 + \sqrt 5)^2 + \sqrt 5 + \sqrt 2\)

Answer 1

Correct option is (1) \(\log[(2 + \sqrt 5)^2 (\sqrt 2 - 1)] - \sqrt 5 + \sqrt 2\)