# Finding the indefinite integral of sin^2(pi*x) cos^5(pi*x)

1. Feb 19, 2016

### grafs50

1. The problem statement, all variables and given/known data
∫(sin2(πx)*cos5(πx))dx.

2. Relevant equations
Just the above.

3. The attempt at a solution
I have no idea how pi effects the answer, so I basically solved ∫(sin2(x)^cos5(x))dx.

∫(sin2(x)*cos4(x)*cos(x))dx
∫sin2(x)*(1-sin2(x))2*cos(x))dx
U-substitution
u = sin x du = -cos x dx

∫(u2*(1-u2)2) -du
-∫(u2*(1-u2)2) du
-∫(u2*(1-2u2+u4) du
-∫(u2-2u4+u6) du

-((u3/3)-(2u5/5)+(u7/7).

When I look up what the antiderivative should be on integral-calculator.com. the minus sign outside of the parentheses disappears, which I can't figure out how.

Can anyone give me some help?

2. Feb 19, 2016

### RUber

If u = sin x then du = cos x, not - cos x.

3. Feb 19, 2016

### LCKurtz

Fix the sign error that RUber pointed out. Then do the original problem the same way but let $u =\sin(\pi x)$.
[Edit:] Fixed typo.

Last edited: Feb 19, 2016
4. Feb 19, 2016

### Staff: Mentor

No doubt just an oversight, but du = cos(x) dx.

5. Feb 29, 2016

### grafs50

Thanks everyone. Figured it out.