Question

how to do you solve ∫ [(x-1)/(x^2+1)]. take note that (x^2)+1

Answer 1

it's u du substitution

Answer 2

first separate the integrals....do integral of x/x^2+1 - integral of 1/x^2+1

Answer 3

now use u du on the first integral letting u be x^2 + 1....take the derivative to get 1/2du=xdx

Answer 4

so you get 1/2 ln(u) and sub back in the x^2+1 for u

Answer 5

just by looking you can see the 2nd integral is tan^-1(x)

Answer 6

so you can piece it together and get 1/2ln(x^2+1)-tan^-1(x)

Answer 7

i think...someone really should verify this...i'm still waking up

Answer 8

lol, thanks, u got it right. just im a lil bit confused on how you get the second integral to be tan^-1(x).

Answer 9

it's just observation....the derivative of tan-1 is 1/x^2+1 from back in calc 1....so you should be able to just see the integral and do the opposite