## anonymous 4 years ago integrate: 2x/(1+x^2)

1. anonymous

i know the answer is ln(1+x^2) but why

2. anonymous

let u = 1+x^2

3. anonymous

= ln (1 + x^2) oh ok this is the rule integral of f'(x) / f(x) = ln f(x)

4. anonymous

$u=x^2+1,du=2xdx,\int\frac{1}{u}du=\ln(u)$

5. anonymous

what jimmyrep said. as for "why" his answer makes more sense, i just showed how to get it

6. amistre64

$Dx(ln(f(x)))=\frac{f'(x)}{f(x)}$

7. anonymous

check by differentiating using chain rule and you will see why u sub works

8. anonymous

Thank you, the u substitution was enough to illustrate the process. I appreciate the help.

9. Hero

Jimmy Rep's general rule is pretty useful too. If anything, you should remember that the next time you run into a similar one. U sub will come naturally when you remember the general rule.

10. anonymous

Yea, I took some time away from this calculus based stuff when I studied linear algebra and so when I came back to it, I panicked and was like is this partial fractions? integration by parts? and I just couldnt figure it out, but I know you guys always come through.