Posted by **APpreciative student** on Monday, November 29, 2010 at 5:34pm.

Hi! Thank you for your help

How do you find the antiderivative of

2/((x^2)+1)

"two over (x squared plus one)"

I think I have to do integration by partial fractions but I didn't figure it out...assistance is much appreciated

Thank you very much

- AP Calc BC -
**MathMate**, Monday, November 29, 2010 at 8:22pm
A standard integral is

∫a/(a²+x²)

=tan^{-1}(x/a) + C

If you have done substitution, you can evaluate the integral by substituting

tan(y)=x/a

sec²(y)dy/dx=1/a, or

dx=asec²(y)dy

then

∫a/(a²+x²)dx

=(1/a)∫dx/(1+tan²(y))

=∫sec²(y)dy/sec²(y)

=y + C

=tan^{-1}(x/a) + C

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