Question

Determine ∫(sin^2 x) (cos^5 x) dx.

Answer 1

The equation should look like this - \[\int\limits (\sin ^{2}x) (\cos ^{5}x) dx\]
And the answer is \[\sin ^{3}x /3 - 2\sin ^{5}x/5 + \sin ^{7}x/7+ c\]

Answer 2

i think the gimmick is you split off a cosine and write
\[\int \sin^2(x) \cos^4(x) \cos(x)dx\]

Answer 3

then write
\[\int \sin^2(x)(1-\sin^2(x))^2 \cos(x)dx\] and now a simple u-sub via
\[u=\sin(x)\] etc

Answer 4

get
\[\int u^2(1-u^2)^2du\] and should be easy from there, yes?

Answer 5

then the answer is : (u^3 + u / 3) + C