Question

please help solve: integral sinx^(5)dx

Answer 1

let \[u=\cos(x)\]
so \[du=-\sin(x) dx\]
thus \[\int\limits_{}^{} \sin^5 (x) dx = \int\limits_{}^{} \sin^4 (x) \sin(x) dx= \int\limits_{}^{} (1- \cos^2(x))^2 \sin(x) dx\]
=\[-\int\limits_{}^{}(1-u^2)^2 du = -\int\limits_{}^{} (1-2u^2+u^4) du\]
I guess you can do the last integral, just remeber to replace u by cos(x) after you done

Answer 2

thank you

Answer 3

u r welcome