Question

Trig integration
HELP PLEASE! step by step:(
Ive been trying to solve this one for 2 hours now

Answer 1

\[\int\limits_{?}^{?}\cos^4xsin^2x\]

Answer 2

indefinite integral

Answer 3

sin and cos are derivatives of each other, so there might be a way to think of this as:\[\int f'(g)g'~dx\to f(g)\]

Answer 4

or using some creative trig identities

Answer 5

but the even exponents might be screwing up the works alittle

Answer 6

try writing sin^2 x as 1-cos^2 x
then you'll have difference of two solvable integrals.

Answer 7

I think youre supposed to use double angle identities but im not sure how.

Answer 8

\[sin(a+a)=sin(a)cos(a)+sin(a)cos(a)\]
\[sin(2a)=2sin(a)cos(a)\]

Answer 9

This is how far I got
\[\int\limits \frac{ 1 }{ 2 }(1-\cos2x)(\frac{ 1 }{ 2 } \sin2x)^2= \frac{ 1 }{ 8 } \int\limits \sin^2 (2x) -\sin^2 (2x)\cos(2x)\]