3 years ago

25 Points! Midterm Today! Can anyone help with this problem?

Mathematics

1 answer:

Andrews [41]3 years ago

6 0

I really do wish I could help But I’m not sure I tried to figure it out and i just can’t get it

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<img src="https://tex.z-dn.net/?f=%20%5Cint%20%5Cfrac%7Bdx%7D%7Bxln%5E%7Bp%7Dx%20%7D" id="TexFormula1" title=" \int \frac{dx}{xl

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$\displaystyle\int\frac{\mathrm dx}{x\ln^px}=\int\frac{\mathrm du}{u^p}=\begin{cases}\dfrac{u^{p+1}}{p+1}+C&\text{for }p\neq1\\\\\ln|u|+C&\text{for }p=1\end{cases}$

Then transforming back to $x$ gives

$\displaystyle\int\frac{\mathrm dx}{x\ln^px}=\begin{cases}\dfrac{\ln^{p+1}x}{p+1}+C&\text{for }p\neq1\\\\\ln|\ln x|+C&\text{for }p=1\end{cases}$

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