Question

Results for 'Integral of((2+x)/(3+x)^2))e^x dx?

Answer 1

`e^x/(3+x)+C`

Explanation:

We want to solve

`int((2+x)*e^x)/(3+x)^2dx`

Integral of this type typical include the exponential integral

However this integral have a neat solution

By the quotient rule for differentiation notice

`(e^x/(3+x))'=(e^x*(3+x)-e^x)/(3+x)^2=((2+x)*e^x)/(3+x)^2`

Exactly the answer we seek, therefore

`int((2+x)*e^x)/(3+x)^2dx=e^x/(3+x)+C`