Waste less time on Facebook — follow Brilliant.
×

Please solve this problem

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

Note by Abhay Raj Singh
2 years, 4 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

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

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

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

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

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 · 2 years, 4 months ago

Log in to reply

@Siddhartha Srivastava thanx Abhay Raj Singh · 2 years, 4 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...