1.
Find dx using reverse chain rule start from u = sin x
2.
Replace in the original expression: sin x to u and dx to your differential.
3.
Notice the denominator turn into cos2 x.
4.
You need everything to be in terms of u to integrate.
5.
Realise you can manipulate u = sin x from the beginning to find cos2 x. Hint: Square both sides and then use sin2 x + cos2 x.
6.
Now you should have everything in terms of u so: (1 + u) / (1 - u2 ) du.
7.
Realise that the denominator is a difference of two squares: (1+ u) / (1 - u)(1 + u)
8.
(1 + u) at the top and bottom cancel out so you are left with simply: 1 / (1 - u)
9.
This integrates to ln |1 - u | + c
10.
Finally u = sin x
11.
Solution: ln |1 - sin x | + c
Last reply 4 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
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Last reply 4 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrong71