What is the integral from 5 to 25 of 1/(x(ln(x))^6) ?

The integral from 5 to 25 of 1/(x(ln(x))^6) is (31)/(160ln^5(5))

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integral from 5 to 25 of 1/(x(ln(x))^6)

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{6}} d x

\frac{31}{160 ln ^{5} ( 5 )}

Decimal

0.01794 \dots

Solution steps

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{6}} d x

Apply u-substitution

= \int_{l n (5)}^{2 l n (5)} \frac{1}{u ^{6}} d u

Apply the Power Rule

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

Compute the boundaries:

\frac{31}{160 ln ^{5} ( 5 )}

= \frac{31}{160 ln ^{5} ( 5 )}

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What is the integral from 5 to 25 of 1/(x(ln(x))^6) ?
The integral from 5 to 25 of 1/(x(ln(x))^6) is (31)/(160ln^5(5))