Mathematics

The value of the integral $$\displaystyle \int^{1/\sqrt{3}}_{1/\sqrt{3}} \dfrac{x^4}{1-x^4} cos ^{-1} \dfrac{2x}{1+x^2} dx$$


ANSWER

$$0$$


SOLUTION
Given,

$$\displaystyle \int _{\tfrac{1}{\sqrt{3}}}^{\tfrac{1}{\sqrt{3}}}\dfrac{x^4}{1-x^4}\cos ^{-1}\left(\dfrac{2x}{1+x^2}\right)dx$$

we have formula,

$$\int _a^af\left(x\right)dx=0,\:a\ne \infty $$

$$=0$$
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Single Correct Medium Published on 17th 09, 2020
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