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Question Number 43324 by Raj Singh last updated on 09/Sep/18

Answered by tanmay.chaudhury50@gmail.com last updated on 09/Sep/18

$$\frac{1}{2}\int \frac{x^2+1+x^2-1}{(x^2-1)(x^2+1)}dx$$$$\frac{1}{2}\int \frac{dx}{x^2-1}+\frac{1}{2}\int \frac{dx}{x^2+1}$$$$\frac{1}{4}\int \frac{(x+1)-(x-1)}{(x+1)(x-1)}dx+\frac{1}{2}\int \frac{dx}{x^2+1}$$$$\frac{1}{4}\int \frac{dx}{x+1}-\frac{1}{4}\int \frac{dx}{x-1}+\frac{1}{2}\int \frac{dx}{x^2+1}$$$$\frac{1}{4}ln\mid \frac{x+1}{x-1}\mid +\frac{1}{2}{tan}^{-1}\left(x\right)+c$$

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