Question

integrate

Answer 1

\[\int\limits_{?}^{?} sinxcos^2x dx\]

Answer 2

\[u=\cos(x)\]

Answer 3

wont there still be an x though?

Answer 4

\[\large\rm \int\limits \sin x (\cos x)^2~dx\]An x where?

Answer 5

\[\cos ^{2}x=\frac{ 1+\cos2x }{ 2 }\]

Answer 6

If you make that substitution, what do you get for your differential?\[\large\rm u=\cos x\]\[\large\rm du=?\]

Answer 7

-sinx

Answer 8

Yes\[\large\rm du=-\sin x~dx\]

Answer 9

Do you see how that helps?
If not I can color code it.

Answer 10

OHH

Answer 11

Oh, now i understand where @zepdrix was going. Use their method.

Answer 12

Sorry i'm not thinking xD Okay thank you for the help!!

Answer 13

Half Angle Identity was a clever idea royal :D
I think the sine gets in the way though.