Another Integration: integral of ( 1 + x ) / ( 1 + x^ 2 ) dx

[grapz]

Indefinite integral of ( 1 + x ) / ( 1 + x^ 2 ) dx

This is what i did


i simplified : 1 + x / ( 1 + x ) ( 1 - x) dx = 1 / 1 -x dx

let u = 1 - x
du = -dx

integral of 1 / u du = - ln | 1 - x | + c


But the answer is

arc tan x + 1/2 ln ( 1 + x ^2 ) + c

Where did i go wrong? Is it because i can not simply the way i did with the integrand?

 

[o_O]

Re: Another Integration problem

\(\displaystyle 1 + x^{2} \neq (1-x)(1+x)\)

It's the DIFFERENCE of squares formula so this doesn't apply here.

Split the fraction into two and you should be able to figure out the rest.