Integration by substitution help please $$
\int_0^{\pi/2} \frac{\sin\theta}{1+\cos\theta} \, d\theta
$$
My working thus far:
$$u=1+\cos\theta$$
$$\text{d}u=-\sin\theta \ \text{d}  \theta$$
Substituting limits in and obtaining them in terms of u:
$$\int^1_2 \frac{\sin\theta}{u} \cdot \frac{-1}{\sin\theta} \ \text{d}u$$
The answer in the back is $\ln(3/2)$. From my limits, I haven't done this right. Where am I going wrong?

I think book has printing mistake. You are doing well and all steps are correct
