Mathematics

# Solve $\displaystyle\int\dfrac{e^x(x-1)}{(x+1)^3}dx$

$\dfrac{{{e^x}}}{{{{\left( {x + 1} \right)}^2}}} + c$

##### SOLUTION
$=\displaystyle\int \dfrac{e^{x}(x-1)}{x+1}^{3}dx$
$=\displaystyle\int \dfrac{e^{x}(x+1)}{(x+1)^{3}}dx-2\int \dfrac{e^{x}}{(x+1)}dx$
$=\displaystyle\int \dfrac{e^{x}dx}{(x+1)^{2}}-2\int \dfrac{e^{x}}{(x+1)^{3}}dx$
Applying integration by  parts on  firsttem
$\dfrac{e^{x}}{(x+1)^{2}}+^{2}\displaystyle\int \dfrac{e^{x}}{(x+1)^{3}}-\int \dfrac{e^{x}}{(x+1)^{3}}+c$
$\dfrac{e^{x}}{(x+1)^{2}}+c.$
$B$ is correct

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

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Let $f$ be a positive function. Let $\displaystyle I_1=\int_{\displaystyle 1-k}^{\displaystyle k}{(x)f(x(1-x))dx}$; $\displaystyle I_2=\int_{\displaystyle 1-k}^{\displaystyle k}{f(x(1-x))dx}$, where $2k-1>0$. Then, $\displaystyle\frac{I_2}{I_1}$ is
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• C. $1$
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The value of $\displaystyle\int _{ 0 }^{ \tfrac { \pi }{ 2 } }{ \frac { \cos ^{ \frac { 5 }{ 3 } }{ x } }{ \cos ^{ \frac { 5 }{ 3 } }{ x } +\sin ^{ \frac { 5 }{ 3 } }{ x } } dx }$ is
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