The value of the integral -1-31-3x41-x4 cos -12x1-x2 dx

The correct option is A 0 Given, ∫ _1√(3)^1√(3)x^41 x^4cos ^ 1(2x1+x^2)dx we have formula, ∫ _a^af(x)dx=0, a∞ =0 ...

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Integration of Piecewise Continuous Functions

The value of ...

Question

The value of the integral $\int_{1 / \sqrt{3}}^{1 / \sqrt{3}} \frac{x^{4}}{1 - x^{4}} c o s^{- 1} \frac{2 x}{1 + x^{2}} d x$

0

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\frac{π}{\sqrt{3}} + l o g \frac{\sqrt{3} + 1}{\sqrt{3} - 1}

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\frac{1}{\sqrt{3}} + \frac{π}{2} l o g \frac{\sqrt{3} + 1}{\sqrt{3} - 1}

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none of these

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\int_{- 1 / \sqrt{3}}^{1 / \sqrt{3}} \frac{x^{4}}{1 - x^{4}} c o s^{- 1} \frac{2 x}{1 + x^{2}} d x =

\int_{- 1 / \sqrt{3}}^{1 / \sqrt{3}} \frac{x^{4}}{1 - x^{4}} {cos}^{- 1} \frac{{2 x}}{1 {+ x}^{2}} d x = k \int_{0}^{1 / \sqrt{3}} \frac{x^{4}}{1 - x^{4}}

k

\int_{\frac{1}{\sqrt{3}}}^{\frac{1}{\sqrt{3}}} \frac{x^{4}}{1 - x^{4}} {cos}^{- 1} \frac{2 x}{1 + x^{2}} d x = k \int_{0}^{\frac{1}{\sqrt{3}}} \frac{x^{4}}{1 - x^{4}} d x

^{'} k^{'}

\int_{0}^{1} s i n^{- 1} (\frac{2 x}{1 + x^{2}}) d x =

3 s i n^{- 1} \frac{2 x}{1 + x^{2}} - 4 c o s^{- 1} \frac{1 - x^{2}}{1 + x^{2}} + 2 t a n^{- 1} \frac{2 x}{1 + x^{2}} = \frac{π}{3}

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