There's different ways you can do a)Please view image attached. Answers have been written in red.
by the second statement he probably means x = sin^2 uThere's different ways you can do a)
You can change to which after expanding will give you an integral with varying powers of (1+x) which you can integrate straight away.
You can also do a u sub by letting and then expanding to get varying powers of which you can also integrate straight away.