How do you integrate $\int \frac{{(5 + ln x)}^{5}}{x}$ $int(5+lnx)^5/x$ using substitution?

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How do you integrate $\int \frac{{(5 + ln x)}^{5}}{x}$ $int(5+lnx)^5/x$ using substitution?

1 Answer

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Answer 1 · 2016-07-23T16:55:09

$\frac{{(5 + ln x)}^{5}}{6} + C$ $(5+lnx)^5/6+C$

Explanation:

Let us take the subst. $(5 + ln x) = t$ $(5+lnx)=t$ , so that, $\frac{1}{x} d x = d t$ $1/xdx=dt$

Hence, $\int \frac{{(5 + ln x)}^{5}}{x} d x = \int t^{5} d t = \frac{t^{6}}{6} = \frac{{(5 + ln x)}^{6}}{6} + C$ $int(5+lnx)^5/xdx=intt^5dt=t^6/6=(5+lnx)^6/6+C$

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How do you integrate $\int \frac{{(5 + ln x)}^{5}}{x}$ $int(5+lnx)^5/x$ using substitution?

1 Answer

Explanation:

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Explanation:

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How do you integrate $\int \frac{{(5 + ln x)}^{5}}{x}$ $int(5+lnx)^5/x$ using substitution?