How Do You Derive the Integral of 1/(x^2 + a^2)?

[Kalie]

Yeah this one is good...

Derive the following:

int(1/(x^2 + a^2)dx = 1/a*arctan(x/a) + C

any idea how I would derive this thing?
Cause I'm totally lost...

 

[quasar987]

Well do you agree that if you show that the derivative of 1/a*arctan(x/a) + C is 1/(x^2 + a^2, then you will have attained your goal?

 

[courtrigrad]

fundamental theorem of calculus

 

[Kalie]

no he actually wants us to plow thorugh the intregal using subsitution and stuff and then somehow end up at the answer

 

[courtrigrad]

use the substitution $$x = a\tan \theta$$