Question

What is the Integral of Sin^6(5x)(cos(5x))dx
Using parts?
Thanks!

Answer 1

Let \[u=sin(5x)\]\[\frac{du}{dx}=5cos(5x)\]\[du=5cos(5x)dx\]thus\[\int_{}{}sin^{6}(5x)cos(5x)dx\]\[=5\int_{}{}u^6du=5\frac{u^7}{7}+c\]\[=\frac{5}{7}sin^{7}(5x)+c\]