Help on Integral

[Bvana]

I am a bit stuck on this Integral, could anyone nudge me in the right direction?
Also, please let me know if my initial work has any mistake.
Thank you!
Benoit

 

[Deleted member 4993]

I am a bit stuck on this Integral, could anyone nudge me in the right direction?
Also, please let me know if my initial work has any mistake.
Thank you!
Benoit

View attachment 14960

\(\displaystyle \frac{u^2}{4+u^2}\)

\(\displaystyle = 1 - \frac{4}{2^2+u^2}\)

continue....

 

[Bvana]

Oh wow, I would have never thought of that. Thank you!

 

[Steven G]

Oh wow, I would have never thought of that. Thank you!

You have to think of that! Whenever you have a rational function (the division of two polynomials) and the degree of the numerator is not smaller than the degree of the denominator you have to do long division from the start.
Also, that is one strange equal sign.