Question

integrate: (x-1)/(x^2 + 1)
I recognize the denominator as arctan but not sure what that gets me?

Answer 1

1/2 ln(x^2+1) - arctan(x)

Answer 2

You can break it up:
\[\large \int\limits\frac{x-1}{x^{2}+1} dx = \int\limits\frac{x}{x^{2}+1} dx -\int\limits\frac{1}{x^{2}+1} dx\]

The integrate it one by one.

Answer 3

The first one is a u sub & the next one is a trig inverse.

Answer 4

I was trying to make it way harder than that lol...dangit

Answer 5

Do you want to do it a hard way? lol