Solve:

Question

du/dt = (sin t) / (u^2 + 1)

So far I got:

arctan u = -ln |csc t + cot t| + C

I'm not sure where to go from there. Thank you so much for the help!

Answer 1

Separate the variables:

(u^2 + 1) du = sin t dt

Now integrate

2/3 u^3 + u = -cos t