How to choose correct trigonometric identity when solving integration questions

Question

For example $\int\frac{sin²x}{1+cosx}$dx

Here I use trigonometric identity:-

sin²x= 1-cos²x

The following integral transforms into

$\int\frac{1-cos²x}{1+cosx}$dx

And now here I have another doubt what kind of substitution should I make?

I always struggle with trigonometric integrals.If you have tips for solving trigonometric integrals please tell me.

Thanks in advance