Question

Integrate (cos(x))^4

Answer 1

Is there a way without the reduction formula?

Answer 2

A quick search gives you hundreds of results with different alternative methods

Answer 3

http://math.stackexchange.com/questions/385938/evaluating-int-cos4x-operatorname-d-x

Answer 4

Here is the method that I like :
\[(\cos x)^4 = \frac{1}{2^4}(e^{ix}+e^{-ix})^4 \]

Expand above using binomial theorem and integrate term by term