what is the integral of cosxln(sinx) dx?

Answer 1

First use substitution.
Let y = sin x, then dy = cos x dx
The integral becomes
ln(y) dy
Now use integration by parts.
Let u = ln(y) and dv = dy, then
du = 1/y dy and v = y
uv - v du
= y ln(y) - integral of [y(1/y) dy]
= y ln(y) - integral of [1 dy]
= ln(y) - y + C
Replace y with sin x

Answer 2

Do your homework by yourself :( posting your worksheet on here isn't fair. These are all u - substitutions.

Answer 3

sin(X) *ln(sin(x))-sin(x)