AP Calc BC

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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 -

    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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