( 1 + x ) 2 x ( 1 + x 2 ) ? d x

Question

$\int \frac{{(1 + x)}^{2}}{x (1 + x^{2})} d x$

Smart Achievers · Accepted Answer

(4)

Ans. $l o g x + 2 t a n^{- 1} x + C$

Explanation

$\int \frac{{(1 + x)}^{2}}{x (1 + x^{2})} d x = \int \frac{(1 + x^{2}) + 2 x}{x (1 + x^{2})} d x$

$= \int (\frac{1}{x} + 2 \cdot \frac{1}{1 + x^{2}}) d x$

$= \int \frac{1}{x} d x + \int \frac{2}{1 + x^{2}} d x$

$= \log x + 2 \tan^{- 1} x + C$

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