( ( x 2 + 2 ) a ( x + tan - 1 x ) x 2 + 1 ) ? d x =

Question

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

Smart Achievers · Accepted Answer

(3)

Ans. $\frac{a^{x + \tan^{- 1} x}}{\log a} + C$

Explanation :

$Put$ $x + \tan^{- 1} x = t$

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

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

$\int [\frac{(x^{2} + 2) a^{(x + \tan^{- 1} x)}}{x^{2} + 1}] d x = \int a^{t} d t$

$= \frac{a^{t}}{\log a} + C$

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

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