Question

integrate cos^10xdx..
.plz show working i really wanna learn these thanks anyway

Answer 1

This has to be done in several steps using integration by parts. To see how it works, take a look at

https://en.wikipedia.org/wiki/Integration_by_reduction_formulae

Answer 2

or, you can expand cos^10(x) as combinations of single powers of cosines:

512 cos^10(x) = 126 + 210cos(2x) + 120cos(4x) + 45cos(6x) + 10cos(8x) + cos(10x)

those terms are easy to integrate. They come from repeated use of

cos(2x) = 2 cos^2(x)-1
cos(4x) = 2cos^2(2x)-1
and so on.