Mathematics

# $\int { \cfrac { \left( x+3 \right) { e }^{ x } }{ { \left( x+4 \right) }^{ 2 } } dx } =$

##### SOLUTION
$I=\int \frac{(x+3)e^{x}}{(x+4)^{2}}dx$
$I=\int \frac{(x+4-1)e^{x}}{(x+4)^{2}}dx$
$I=\int \frac{e^{x}}{(x+4)}dx-\int \frac{e^{x}}{(x+4)^{2}}dx$
$I=\int \frac{e^{x}}{(x+4)}dx-e^{x}[\frac{-1}{(x+4)}]-\int e^{x}(\frac{-1}{(x+4)})dx$
$I=\int \frac{e^{x}dx}{(x+4)}+[\frac{e^{x}}{(x+4)}]-\int \frac{e^{x}}{(x+4)}dx$
$I=\frac{e^{x}}{x+4}+c$

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

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