Integrate me if you can(or like)

[mooncrater]

The question is attached .

N/A

I tried to integrate it using cos^2x=t
But it didn't work . The numerator is killing me.
Euler's equations are not applicable here . Therefore they don't work here . Thus how to solve it ?

 

[Orodruin]

I tried to integrate it using cos^2x=t

Please do not simply state that you tried. Show us your attempt!

 

[mooncrater]

Please do not simply state that you tried. Show us your attempt!

Earlier I tried this question a time or two but now it seems to me I was not doing it clearly and was repeating the same mistake again and again ...
So I tried it again and boom!
Its done. Still, I have attached the attempt that was needed. Thank you for asking me to post the attempt.
Though I have left the integral at a easily solvable step that I know to solve ..
Moreover is there any easier way out of this problem ?