# What is the integral of #int sin^4(x) dx#?

##### 1 Answer

#### Answer

#### Answer:

#### Explanation

#### Explanation:

#### Answer:

#### Explanation:

This integral is mostly about clever rewriting of your functions. As a rule of thumb, if the power is even, we use the double angle formula. The double angle formula says:

If we split up our integral like this,

We can use the double angle formula twice:

Both parts are the same, so we can just put it as a square:

Expanding, we get:

We can then use the other double angle formula

to rewrite the last term as follows:

I will call the left integral in the parenthesis Integral 1, and the right on Integral 2.

**Integral 1**

Looking at the integral, we have the derivative of the inside,

If we let

**Integral 2**

It's not as obvious here, but we can also use u-substitution here. We can let

**Completing the original integral**

Now that we know Integral 1 and Integral 2, we can plug them back into our original expression to get the final answer:

Describe your changes (optional) 200