u-substitution, indefinite integrals I've looked on the web for an answer to this question, and could not find an example.
Could you push me towards a proper u substitution for the following integral? Please don't solve the problem just state what you would use as a substitution and why.
$$\int(\sin^{10}x \cdot \cos x)\ dx$$
My sad attempt
let $$u=\sin x$$
$$du=\cos{x}\ dx$$
$$\int(\sin^{9}x) du$$
should I use trigonometric identities or is another substitution valid?
This question is in the substitution section of the textbook, so it has to be solved with simple substitution
Thanks.

thanks to u/justpassingthrough
$$\int(sin^{10}x*cosx)dx$$
let $$u=sinx$$
$$du=cosx$$
$$\int(sin^{10}x*cosx)dx=\int(u^{10})du$$
$$=\frac{1}{11}u^{11}+C=\frac{1}{11}(sinx)^{11}+C$$
cool
