How to integrate 1/(x^2 +1)^2, does partial fractions work?

[timjones007]

how do you integrate 1/(x² + 1)² ?


i have tried integration by partial fractions but when you set 1 equal to (Ax +B)(x²+1) + (Cx + D) this leads to A=B=C=0 and D=1 which just gives you the original equation

 

[TheFurryGoat]

Try subbing x=tan(u), dx=1/cos^2(u)

 

[cap.r]

here is a quick wiki i found for with general trig substitution laws when you are integrating. the second demonstration is what you need.
http://en.wikipedia.org/wiki/Trigonometric_substitution

 

[Count Iblis]

Partial fraction in terms of the complex linear fractions 1/(x±i) and 1/(x±i)^2 will also work. You can then take together terms with their complex conjugate and then rewrite everything in a manifestly real form (you need to use the relation between the logarithm and arctan etc.).

 

[timjones007]

ah thank you that works