Tuesday

March 31, 2015

March 31, 2015

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

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 didnt figure it out...assistance is much appreciated

Thank you very much

- AP Calc BC -
**MathMate**, Monday, November 29, 2010 at 8:22pmA 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

**Answer this Question**

**Related Questions**

Calc easy - Having trouble getting the correct solution. The integral of “x ...

Calculus B - The Antiderivative of: (2x+3)/((x^3)+3x) This one is devinately ...

MATHS - Prove that one over one squared plus one over two squared plus one over ...

Maths-Integration by Partial Fraction - Use integration by partial fractions to ...

math - Write an explicit formula for the sequence one-half, three-sevenths, one-...

calc - evaluate the integral: y lny dy i know it's integration by parts but i ...

Partial Fractions - I think- and this is just out loud- that you would do (Cx + ...

Calculus - Integration - I came across this problem in my homework, and I was ...

antiderivatives - i need the antiderivative of 2x/x^2 thanks. Two x over x ...

Calc II - Perform long division on the integrand, write the proper fraction as a...