What is int cos^6x dx?
1 Answer
Explanation:
We can rewrite this function as;
Now we can rewrite
If we expand the expression we can get rid of the exponent.
We can split up this expression using the sum rule.
The first integral is pretty straight forward. For the second, use the substitution
The remaining integrals are a little more involved.
We can use the half angle formula again to simplify the 3rd integral.
Use substitution again to solve the second integral.
The last integral should be split up first.
Now we can use the Pythagorean theorem to replace
To solve the remaining integral, use the substitution
Plug the solved integrals into the original expression to get;
Simplify by combining like terms.