What's the integral of 12x/(x^2+1)

What's the integral of 12x/(x^2+1)?

∫ 12x/(x² + 1) dx

Let u = x² + 1. Then,

du/dx = 2x dx
du = 2x dx

So:

∫ (2x dx)6/u
= ∫ 6/u du
= 6 ∫ 1/u du

Finally, we obtain:

6ln|u| + c
= 6ln(x² + 1) + c

I hope this helps!

take x^2+1=t
differentiating , 2x.dx=dt

Now substitute in integral ∫ (6.dt)/t = 6.(ln|t|+c1)
Now substitute t back to x^2+1
so we get the answer as 6.ln(x^2+1)+c2

int(12*x/(x^2 + 1), x) = 6*ln(x^2 + 1) + C

INTEGRAL(12x/(1+x^2) dx]
u=1+x^2 then du=2x dx and then 12x dx=6 du
INTGERAL[6/u du]
=6 ln u + C
=6 ln(1+x^2) +C

hint: u = x^2 + 1