Question

What is the indefinite integral of (1+x)/(1+x^(2)) * dx?

Answer 1

Can it be x + tan^(-1)(x) + c?

Answer 2

No, no, no. Hint: \[ \dfrac {1+x}{1+x^2} = \dfrac {1}{1+x^2} + \dfrac {x}{1+x^2}. \]The derivative of the first of these fractions is simply \[ \tan^{-1} (x). \]The integral of the second fraction is not x. You need a substitution of 1 + x^2 there. In the end, you add the constant of integration. Can you solve it from this point?

Answer 3

Hmm, I know that's tan^(-1)(x), but I don't know what to do from there. I thought my answer could be close.

Answer 4

Did you understand what I said about the u-substitution for the second part? Which part are you having trouble with?

Answer 5

Working on it, I will let you know if I get it. I think I know what to do

Answer 6

All the best! :)

Answer 7

Hmm. A bit stuck here, this is what I have:
u = 1 + x^(2)
du = 2x dx
du/2 = xdx
When using substitution next, how would it be?

Answer 8

The result of that substitution is: \[ \int \dfrac {\mathrm{d}u}{2u}. \] Do you see how I got that? And do you know how to integrate that and put the result in terms of x? That's basically all the rest that you need to know. Good luck with that!

Answer 9

What about the 1 on top? from 1+x