1. ## integral

intergral x((2x)/(x^2+1))dx
Somebody mentioned a sub u= x^2+1 so it is then ln (x^2+1) but what about the x in front of the problem

2. Originally Posted by Bust2000
X ((2x)/(X^2+1))dx
Somebody mentioned a sub u= x^2+1 so it is then ln (x^2+1) but what about the x in front of the problem
do you know hot to do the substitution?

if $\displaystyle u = x^2 + 1$ then $\displaystyle du = 2x \, dx$

3. Hello, Bust2000

X ((2x)/(X^2+1))dx
Check the original problem again . . .

Is that really an $\displaystyle x$ in front?
. . Could it be somebody's multiplication-sign?

Why wasn't the problem presented as: .$\displaystyle \int \frac{2x^2}{x^2+1}\,dx$

4. ## Yes really an x in front

yes there really is an x in front not a multiplication sign

5. If it's really $\displaystyle \int \frac{2x^2}{x^2 + 1}~dx$,

$\displaystyle 2\int \frac{x^2}{x^2 + 1}~dx$

$\displaystyle \frac{x^2}{x^2 + 1} = 1-\frac{1}{x^2 + 1}$

So it becomes, $\displaystyle 2 \left ( \int 1~dx - \int \frac{1}{x^2+1}~dx \right )$

$\displaystyle 2 \left ( x - \text{Arctan}x \right )$

$\displaystyle 2x - 2\text{Arctan}x$