Question

int cosxsinx dx

Answer 1

integral cos(x) sin(x) dx
We simply use substitution.
Let u = sin(x)
Thus du = cos(x) dx
Rewriting,
= integral (u du)
= (1/2)*u^2 + C
= (1/2)*sin^2 (x) + C

Or you may also use substitute the formula sin(2x) = 2sin(x)cos(x) to the original, and then directly integrate.

Hope this helps~ :3

Answer 2

Or

following Jai's method.
let u = cosx
etc

to get

(-1/2) cos^2 x + c