d x ( x 2 + 1 ) ( x 2 + 4 ) =

Question

$\int \frac{d x}{(x^{2} + 1) (x^{2} + 4)} =$

Smart Achievers · Accepted Answer

(3)

Ans. $\frac{1}{3} \tan^{- 1} x - \frac{1}{6} \tan^{- 1} \frac{x}{2} + C$

Explanation :

$\int \frac{d x}{(x^{2} + 1) (x^{2} + 4)} = \frac{1}{3} [\int \frac{d x}{x^{2} + 1} - \int \frac{d x}{x^{2} + 4}]$

$= \frac{1}{3} [\tan^{- 1} x - \frac{1}{2} \tan^{- 1} \frac{x}{2}] + C$

$= \frac{1}{3} \tan^{- 1} x - \frac{1}{6} \tan^{- 1} \frac{x}{2} + C$

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