"The value of definite integral $\int_{\frac{-1}{\sqrt{3}}}^{\frac{1}{\sqrt{3}}} \frac{\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)}{e^{x}+1} d x$ is equal to:

(b) $\frac{\pi}{\sqrt{3}}$

(c) $\frac{\pi}{4 \sqrt{3}}$

(d) $\frac{\pi}{3 \sqrt{3}}$"

Question

"The value of definite integral $\int_{\frac{-1}{\sqrt{3}}}^{\frac{1}{\sqrt{3}}} \frac{\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)}{e^{x}+1} d x$ is equal to:

(b) $\frac{\pi}{\sqrt{3}}$

(c) $\frac{\pi}{4 \sqrt{3}}$

(d) $\frac{\pi}{3 \sqrt{3}}$"

Vineet Loomba · Accepted Answer

"(c) $\frac{\pi}{4 \sqrt{3}}$(c) $\frac{\pi}{4 \sqrt{3}}$

(c) $\frac{\pi}{4 \sqrt{3}}$(c) $\frac{\pi}{4 \sqrt{3}}$

(c) $\frac{\pi}{4 \sqrt{3}}$(c) $\frac{\pi}{4 \sqrt{3}}$(c) $\frac{\pi}{4 \sqrt{3}}$"

Solution