Extension Integration Questions (1 Viewer)

[luo_ge]

I was just wondering on how to do these questions, there are no worked examples in my textbook. Any help would be greatly appreciated.

 

[InteGrand]

I was just wondering on how to do these questions, there are no worked examples in my textbook. Any help would be greatly appreciated.

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View attachment 33814

Use the reverse chain rule or substitution (let u equal the quadratic that appears).

 

[pikachu975]

I was just wondering on how to do these questions, there are no worked examples in my textbook. Any help would be greatly appreciated.

View attachment 33813

View attachment 33814

First one:
Integrate x/(x^2 -1)^2
let u = x^2 - 1
du = 2xdx
dx = du/2x

=> 1/2(u^2)
Should be easy to integrate this and sub back in

Second one:
u=x^2 + 1
du = 2xdx
dx = du/2x

Should be easy to integrate from there and sub back in