# Thread: Integrating Problem help.

1. ## Integrating Problem help.

$\int \frac{1-x^2}{1+x^2}.dx$

Please help me, I couldnt solve it. Thank you

2. Originally Posted by whitepenguin
$\int \frac{1-x^2}{1+x^2}.dx$

Please help me, I couldnt solve it. Thank you
Note that $\frac{1-x^2}{1+x^2} = -1 + \frac{2}{x^2 + 1}$.

3. Originally Posted by whitepenguin
$\int \frac{1-x^2}{1+x^2}.dx$

Please help me, I couldnt solve it. Thank you
Break it down

$=\int\frac{1}{1+x^2}+\int\frac{x^2}{1+x^2}$.

For the first, look for the $\arctan{x}$

For the second, divide...

4. Originally Posted by VonNemo19
Break it down

$=\int\frac{1}{1+x^2}+\int\frac{x^2}{1+x^2}$.

For the first, look for the $\arctan{x}$

For the second, divide...
Actually it's $\int{\frac{1}{1 + x^2}\,dx} - \int{\frac{x^2}{1 + x^2}\,dx}$.

5. , How come I coulnt think of that. It's really simple

Thank you

6. Originally Posted by Prove It
Actually it's $\int{\frac{1}{1 + x^2}\,dx} - \int{\frac{x^2}{1 + x^2}\,dx}$.
What am I...like -3 now?