# How do you integrate #f(x)=5/(4x^3+4)# using the quotient rule?

##### 1 Answer

The quotient rule applies to differentiation; not integration. The given function must be integrated using partial fraction expansion, variable substitution, and trigonometric substitution.

#### Explanation:

Expand

Note: I would have taken you, step-by-step, through the expansion but it made the explanation too long.

Break into two integrals:

Multiply the second integral by

Break the second integral into two integral so that the numerator of the first is

Simplify the third integral:

The first integral is the natural logarithm:

A variable substitution makes the second integral become the natural logarithm, too:

A trigonometric substitution makes the second integral become the inverse tangent: