∫dxx(log⁡x)m is equal to

# $\int \frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{log}\mathrm{x}{\right)}^{\mathrm{m}}}$ is equal to

1. A

$\frac{\left(\mathrm{log}\mathrm{x}{\right)}^{\mathrm{m}}}{\mathrm{m}}+\mathrm{C}$

2. B

$\frac{\left(\mathrm{log}\mathrm{x}{\right)}^{\mathrm{m}-1}}{\mathrm{m}-1}+\mathrm{C}$

3. C

$\frac{\left(\mathrm{log}\mathrm{x}{\right)}^{1-\mathrm{m}}}{1-\mathrm{m}}+\mathrm{C}$

4. D

$\frac{\left(\mathrm{log}\mathrm{x}{\right)}^{1-\mathrm{m}}}{\mathrm{m}}+\mathrm{C}$

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### Solution:

Here, given integrand is not in any standard form. So,we convert it by substitution method in a standard form and then integrate it.

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