∫sin^3(x)cos^2(x)dx.
I know you have to use the sin rule where you can change the sin into a 1-cos.
I'm not sure how to utilize that.
I've done u substitution where u=cos(x) and du=sin(x) but that's as far as I got before I was stuck.
Thanks!
∫sin^3(x)cos^2(x)dx.
I know you have to use the sin rule where you can change the sin into a 1-cos.
I'm not sure how to utilize that.
I've done u substitution where u=cos(x) and du=sin(x) but that's as far as I got before I was stuck.
Thanks!
$\displaystyle \int \sin^3(x)cos^2(x)dx$
$\displaystyle \int \sin(x)\sin^2(x)\cos^2(x)dx$
$\displaystyle \int \sin(x)(1-\cos^2(x))\cos^2(x)dx$
$\displaystyle \int \sin(x)(\cos^2(x)-\cos^4(x))dx$
$\displaystyle u = \cos(x) $
$\displaystyle -du = \sin(x) $
$\displaystyle -\int (u^2-u^4)du$
$\displaystyle \int (u^4-u^2)du$