Please solve this problem

\int { \frac { { \left( x+3 \right) e }^{ x } }{ (x+5)^{ 3 } } dx }

#Calculus #Integration #IndefiniteIntegral

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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Comments

$\int { \frac { { \left( x+3 \right) e }^{ x } }{ (x+5)^{ 3 } } dx }$

$= \int \frac { ( x+5 - 2) e^x }{ (x+5)^3 } dx$

$= \int \frac { (x+5) e^x }{ (x+5)^3 } dx + \int \frac { - 2 e^x }{ (x+5)^3 } dx$

$= \int \frac { e^x }{ (x+5)^2 } dx + \int \frac { - 2 e^x }{ (x+5)^3 } dx$

Using IBP on the second integral with $u = e^x$ and $dv = \frac{- 2}{(x+5)^3}$

$= \int \frac { e^x }{ (x+5)^2 } dx + \frac{e^x}{(x+5)^2} -\int \frac { e^x }{ (x+5)^2 } dx$

$= \frac{e^x}{(x+5)^2}$

Siddhartha Srivastava - 6 years, 2 months ago

thanx

Abhay Raj Singh - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$