Integrate, by using substitution: 2 x dx / (1+x^2)^3?

Question

Please show how you came to the answer. Thanks!

Answer 1

I = ∫ (2x) / (1 + x²) ³ dx
Let u = 1 + x²
du = 2x dx
I = ∫ (1 / u ³ ) du
I = ∫ u^(- 3) du
I = u^(-2) / (-2) + C
I = (-1/2) / [ ( 1+x ² ) ² ] + C

Answer 2

int { 2x/(1 + x^2)^3 } dx

let u = 1 + x^2
du = 2x dx

= int { 1/(u^3) } du
= int { u^(-3) } du
= u^(-2)/(-2) + C
= -1/(2u^2) + C
= -1/(2(1+ x^2)^2) + C