# When would you use u substitution twice?

##### 1 Answer

Jul 1, 2015

When we are reversing a differentiation that had the composition of three functions. Here is one example.

#### Explanation:

Let

To avoid using

Let

We the integrate and back-substitute:

# = 1/35 sin^5u +C#

# = 1/35 sin^5 7x +C#

If we check the answer by differentiating, we'll use the chain rule twice.

# = 5(sin(7x))^4*cos(7x)d/dx(7x)#

# = 5(sin(7x))^4*cos(7x)*7#