anonymous
  • anonymous
integrate: 2x/(1+x^2)
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
i know the answer is ln(1+x^2) but why
anonymous
  • anonymous
let u = 1+x^2
anonymous
  • anonymous
= ln (1 + x^2) oh ok this is the rule integral of f'(x) / f(x) = ln f(x)

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anonymous
  • anonymous
\[u=x^2+1,du=2xdx,\int\frac{1}{u}du=\ln(u)\]
anonymous
  • anonymous
what jimmyrep said. as for "why" his answer makes more sense, i just showed how to get it
amistre64
  • amistre64
\[Dx(ln(f(x)))=\frac{f'(x)}{f(x)}\]
anonymous
  • anonymous
check by differentiating using chain rule and you will see why u sub works
anonymous
  • anonymous
Thank you, the u substitution was enough to illustrate the process. I appreciate the help.
Hero
  • 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.
anonymous
  • 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.

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