1. ## Integration by Parts?

If $\int$ udv = uv - $\int$ vdu

then how does

I just don't see why the last part the 48cos(t/4), did not stay as the sine.

2. Originally Posted by gammaman

If $\int$ udv = uv - $\int$ vdu

then how does

I just don't see why the last part the 48cos(t/4), did not stay as the sine.
Because $\int \sin \frac t4 ~dt=-4 \cos \frac t4+c$

3. Oh I see, because of the $\int$ after the minus sign, I must still integrate and change the sine to cosine, right?

4. Originally Posted by gammaman
Oh I see, because of the $\int$ after the minus sign, I must still integrate and change the sine to cosine, right?
Yes

(I made a small typo, the integral of sine is -cosine)