# How do you integrate #int5xsqrt(2x+3)# using substitution?

##### 1 Answer

#### Explanation:

This integral doesn't seem quiet obvious, so I will go through all the steps in high detail.

When evaluating integrals, it is sometimes a matter of trial and error, especially when it comes to u-substitutions.

For this particular integral, we may choose

If

Solving

We can, however, pull out a

Proceeding with the integration process, we can now rewrite our integral.

If we multiply everything into the parentheses and simplify we get

#=1/2u^(5/2) - 5/2 u^(3/2)+C#

#=1/2(2x+3)^(5/2) - 5/2(2x+3)^(3/2) + C#