Question

integrate[sin^2(x)cos^4(x)]

Answer 1

Even powers? oo this one is going to be a doozy!

Answer 2

You can use the `Half-Angle Identities` a bunch of times.
Or another method is to use the `Reduction Formula`.

Are you familiar with the Cosine Reduction Formula? It's really convenient.

Answer 3

the half angle yes, what's the cosine reduction formula?

Answer 4

\[\Large\bf\sf \int\limits \cos^n x\;dx \quad=\quad \frac{1}{n}\cos^{n-1}x \sin x+\frac{n-1}{n}\int\limits \cos^{n-2}x\;dx\]

Answer 5

It lowers the exponent by 2 each time we apply it.

Answer 6

i'm coming up with
\[\frac{ x }{ 16 }+\frac{ \sin2x }{ 32 }+\frac{ \sin^3[2x] }{ 48 }\]

Answer 7

but that doesnt check out and i cant see the flaw in my process