Mathematics

$\displaystyle\int { \dfrac { \left( x+3 \right) { e }^{ x } }{ { \left( x+4 \right) }^{ 2 } } } dx$ is equal to

$\dfrac { { e }^{ x } }{ x+4 } +C$

SOLUTION
$I=\displaystyle\int { \dfrac { (x+3){ e }^{ x } }{ { (x+4) }^{ 2 } } dx }$

$=\displaystyle\int { \dfrac { (x+4-1){ e }^{ x } }{ { (x+4) }^{ 2 } } dx }$

$=\displaystyle\int { \dfrac { { e }^{ x } }{ { (x+4) } } dx }$$-\displaystyle\int { \dfrac { { e }^{ x } }{ { (x+4) }^{ 2 } } dx } =\dfrac{e^x}{x+4}+\displaystyle\int { \dfrac { { e }^{ x } }{ { (x+4)^2 } } dx }$$-\displaystyle\int { \dfrac { { e }^{ x } }{ { (x+4) }^{ 2 } } dx }$ [ Using method of by parts]

$=\dfrac{e^x}{x+4}+c$ [ Where $c$ is integrating constant].

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

Realted Questions

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