Evaluate the definite integral please help

the integral is cost/(1+sint)dt the limit is from 0 to pi/2
can you please explain this problem because i have a feeling it will be on my exam

∫cost(t) / 1+sin(t) dt from o to π/2

Use a u substitution

u = 1+sin(t) dt
du = cos(t) dt

∫ du / u

ln[u] from o to π/2

Plug in 1+sin(t) for u and then the limits...

ln[1+sin(t)]

ln[1+sin(π/2)] - ln[1+sin(0)]

ln2 - 0

Final Answer
ln[2]