Question

Integrate sin^9(x)dx

Answer 1

The first you want to do is derive a reduction formula:
\[ \int \sin^n x \ dx = (something) + (constant) \int \sin^{n-2} x \ dx \]
To do this, use integration by parts.

Once you have it, use it to step down your integral sin^9 --> sin^7 --> sin^5 etc.

Answer 2

make sense? Do you know how to do this?

Answer 3

or perhaps you want to strip out a sinx giving\[\sin^8x \sin x=(1-\cos^2x)^4\sin x\]then you can just expand and integrate with a simple u-substitution.