## anonymous 4 years ago $\int \frac{x}{x^2+1}dx$

1. phi

this (almost) looks like u^-1 du

2. anonymous

This smells of parts, but I'm having trouble with $\int\limits \frac{1}{x^2+1}dx$

3. sirm3d

that is arctangent

4. anonymous

Although that might not help

5. sirm3d

can you enlighten us with the problem?

6. klimenkov

Do a substitution $$u=x^2, du=2xdx$$

7. anonymous

$0.5 \ln(u+1)$

8. anonymous

@sirm3d It's halfway through the DE of my last question

9. klimenkov

Yes. Now make the inverse substitution.

10. sirm3d

hmm, can we try reduction of order with $y=v(ix)$