What is the integral from 5 to 25 of 1/(x(ln(x))^7) ?

The integral from 5 to 25 of 1/(x(ln(x))^7) is (21)/(128ln^6(5))

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integral from 5 to 25 of 1/(x(ln(x))^7)

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{7}} d x

\frac{21}{128 ln ^{6} ( 5 )}

Decimal

0.00943 \dots

Solution steps

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{7}} d x

Simplify

= \int_{5}^{25} \frac{1}{x ln ^{7} ( x )} d x

Apply u-substitution

: \int_{l n (5)}^{2 l n (5)} \frac{1}{u ^{7}} d u

= \int_{l n (5)}^{2 l n (5)} \frac{1}{u ^{7}} d u

Apply the Power Rule

: [- \frac{1}{6 u ^{6}}]_{l n (5)}^{2 l n (5)}

= [- \frac{1}{6 u ^{6}}]_{l n (5)}^{2 l n (5)}

Compute the boundaries:

\frac{21}{128 ln ^{6} ( 5 )}

= \frac{21}{128 ln ^{6} ( 5 )}

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What is the integral from 5 to 25 of 1/(x(ln(x))^7) ?
The integral from 5 to 25 of 1/(x(ln(x))^7) is (21)/(128ln^6(5))