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jaycampos21
jaycampos21 jaycampos21
  • 02-02-2017
  • Mathematics
Answered

#4. I'm not sure whether I should use u substation or basic antiderivative process.

4. I m not sure whether I should use u substation or basic antiderivative process. class=

Verified Answer :

LammettHash
LammettHash LammettHash
  • 09-02-2017

\(\displaystyle\int\frac{\ln x^7}x\,\mathrm dx=7\int\frac{\ln x}x\,\mathrm dx\)

Set \(y=\ln x\), recalling that \(\mathrm dy=\dfrac{\mathrm dx}x\), so the integral is

\(\displaystyle7\int y\,\mathrm dy=\dfrac72y^2+C=\dfrac72(\ln x)^2+C\)

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