integrate: 2x/(1+x^2)

Question

anonymous · Answer

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

anonymous · Answer

let u = 1+x^2

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

hero · Answer

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.

anonymous · Answer

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.