What is the integral from 5 to 25 of 1/(x(ln(x))^5) ?

The integral from 5 to 25 of 1/(x(ln(x))^5) is (15)/(64ln^4(5))

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integral from 5 to 25 of 1/(x(ln(x))^5)

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{5}} d x

\frac{15}{64 ln ^{4} ( 5 )}

Decimal

0.03493 \dots

Solution steps

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{5}} d x

Apply u-substitution

: \int_{l n (5)}^{2 l n (5)} \frac{1}{u ^{5}} d u

= \int_{l n (5)}^{2 l n (5)} \frac{1}{u ^{5}} d u

Apply the Power Rule

: [- \frac{1}{4 u ^{4}}]_{l n (5)}^{2 l n (5)}

= [- \frac{1}{4 u ^{4}}]_{l n (5)}^{2 l n (5)}

Compute the boundaries:

\frac{15}{64 ln ^{4} ( 5 )}

= \frac{15}{64 ln ^{4} ( 5 )}

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What is the integral from 5 to 25 of 1/(x(ln(x))^5) ?
The integral from 5 to 25 of 1/(x(ln(x))^5) is (15)/(64ln^4(5))