Hard integration by substitution exam question

You've got the right start to it. Firstly, you need to change the limits so they're in terms of theta when you're substituting.

So for where you are, you root it and multiply so the next line is integral[4cos^2(theta)], which to integrate you use the double angle identity for cos.

4cos^2(theta) = 2cos(2theta)+2, and integrate that normally and substitute your limits in terms of theta.

Thanks. Just one thing, I’m stuck on using the double angle formula for changing 4cos^2(theta)