Maximizing Integration Expansion | Homework Solution

[yecko]

Homework Statement

https://holland.pk/uptow/i4/d6adf6b4297ef9c8c20c3e58ec66535d.png

Homework Equations

integration

The Attempt at a Solution

[/B]
https://holland.pk/uptow/i4/36ea9fcf0a17f1ea8137f0140c881289.jpg

I have got stuck at this step...
And have no idea on how to go on to the form suggested in the question.
Can anyone tell me how to do this question?
Thank you very much!

 

[Ray Vickson]

Homework Statement

View attachment 203672
https://holland.pk/uptow/i4/d6adf6b4297ef9c8c20c3e58ec66535d.png

Homework Equations

integration

The Attempt at a Solution

View attachment 203673 [/B]
https://holland.pk/uptow/i4/36ea9fcf0a17f1ea8137f0140c881289.jpg

I have got stuck at this step...
And have no idea on how to go on to the form suggested in the question.
Can anyone tell me how to do this question?
Thank you very much!

PF rules forbid us from telling you how to do the question; we can offer hints only. My hint is: try a different integration by parts, because the one you used does not work.

 

[yecko]

Indeed I have tried x-3, sqrt(x-3), x^n
All of the mentioned just do not help me in simplifying the equation, things just get more complicated...
That's the reason I believe I have done the wrong thing in the calculation...

 

[ehild]

You can not integrate (u²-3)ⁿ as you did. Write it as (u²-3)^n-1*u * u and try integration by parts.