amyna
  • amyna
find the intergal:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amyna
  • amyna
|dw:1441078962329:dw|
freckles
  • freckles
let u=ln(x)
freckles
  • freckles
\[\int\limits \tan(\ln(x) ) \cdot \frac{1}{x} dx \\ \text{ notice: the derivative of } \ln(x) \text{ w.r.t. } x \text{ is } \frac{1}{x} \]

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amyna
  • amyna
ok then do i write tan as sin/cos?
freckles
  • freckles
yes
freckles
  • freckles
you write tan(u) as sin(u)/cos(u)
freckles
  • freckles
you can use another sub v=cos(u) so dv=-sin(u) du
amyna
  • amyna
|dw:1441079278529:dw|
freckles
  • freckles
why is dx/x still there
amyna
  • amyna
oh ya i mean du
amyna
  • amyna
so is the answer sin(1/x) / cos (1/x) ??
amyna
  • amyna
+c
freckles
  • freckles
\[\int\limits \frac{\sin(u)}{\cos(u)}du = \int\limits \frac{-dv}{v}=-\ln|v|+C \\ \text{ where } v=\cos(u)\]
freckles
  • freckles
and then replace u
amyna
  • amyna
ok got it thanks!

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