Mathematics

# Integrate:$\int \dfrac{x+2^x.\log 2}{x^2+2^{x+1}}dx$

##### SOLUTION
$I=\displaystyle\int\dfrac{x+2^{x}.\log 2}{x^{2}+2^{x+1}}dx$

Let $u=x^{2}+2^{x+1}$

$\Rightarrow du=2x+2^{x+1}\log 2dx$
$=2(x+2^{x}\log 2)dx$

Substituting

$I=\displaystyle\int\dfrac{du}{2u}$\$

$=\dfrac{1}{2}\log u+C$

$I=\dfrac{1}{2}\log (x^{2}+2^{x+1})+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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