Question

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

Answer 1

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