The math help thread

To further append on, I'd like to take the general case for


Usually, one put this into three different cases: When m is odd, when m is even and n odd, and when m and n are even.

For the first case, m is odd. We can thus represent m = 2k + 1. Remembering the identity

we obtain the following:


Then we just combine the single sin with dx, and set sin x dx = -d(cos x)

For the second case, use the exact same way. Just swap cos and sin, and set cos x dx = d * sin x

For the third case, we'll should use another identity:


Then, just substitute this in, and there you go.

Noah