Can I have some help with this question?

Question

∫ (cosθ/1+sinθ)dθ. Upper limit = π/2 and lower limit =-1.

Answer 1

Let U= sint+1

Then dU = cos t dt

The integral becomes: dU/ U

which integrates to ln U

The anti-derivative is ln [ sin t +1]

Upper limit: ln [ sin pi/2 + 1]

= ln [ 1+1]=ln 2

Lower limit is just ln [ sin -1 +1]

Per property of logs, subtracting these limits:

Ln [ 2/( sin -1 +1)]

Sine is even function, so

Ln [ 2/( 1 - sin 1)]