First slide

Methods of integration

Question

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

Moderate

A

$\frac{1}{3} \tan^{- 1} x - \frac{2}{3} \tan^{- 1} \frac{x}{2} + c$
B

$- \frac{1}{3} \tan^{- 1} x - \frac{2}{3} \tan^{- 1} (\frac{x}{2}) + c$
C

$- \frac{1}{3} \tan^{- 1} x + \frac{2}{3} \tan^{- 1} \frac{x}{2} + c$
D

$\frac{1}{3} \tan^{- 1} x + \frac{2}{3} \tan^{- 1} (x) + c$

Solution

$Let x^{2} = y Split in to partial fractions$
$\int \frac{1}{3} [\frac{4}{x^{2} + 4} - \frac{1}{x^{2} + 1}] d x = \frac{2}{3} \tan^{- 1} \frac{x}{2} - \frac{1}{3} \tan^{- 1} x + c$

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