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Yuki888 [10]
3 years ago
13

What function is not linear?

Mathematics
1 answer:
vlabodo [156]3 years ago
5 0

Answer:

I can't get the thing to copy or put a picture down. But, I think the answer is   C. I'm not good at math. But, Lemme know if I have that one wrong!

- Martiinez ;)

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3 years ago
<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
Eva8 [605]
Substitute u=\ln x, so that \mathrm du=\dfrac{\mathrm dx}x. The integral is then equivalent to

\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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