What is the integral from 7 to 49 of 1/(x(ln(x))^7) ?

The integral from 7 to 49 of 1/(x(ln(x))^7) is (21)/(128ln^6(7))

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integral from 7 to 49 of 1/(x(ln(x))^7)

\int_{7}^{49} \frac{1}{x ( ln ( x ) ) ^{7}} d x

\frac{21}{128 ln ^{6} ( 7 )}

Decimal

0.00302 \dots

Solution steps

\int_{7}^{49} \frac{1}{x ( ln ( x ) ) ^{7}} d x

Simplify

= \int_{7}^{49} \frac{1}{x ln ^{7} ( x )} d x

Apply u-substitution

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

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

Apply the Power Rule

: [- \frac{1}{6 u ^{6}}]_{l n (7)}^{2 l n (7)}

= [- \frac{1}{6 u ^{6}}]_{l n (7)}^{2 l n (7)}

Compute the boundaries:

\frac{21}{128 ln ^{6} ( 7 )}

= \frac{21}{128 ln ^{6} ( 7 )}

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What is the integral from 7 to 49 of 1/(x(ln(x))^7) ?
The integral from 7 to 49 of 1/(x(ln(x))^7) is (21)/(128ln^6(7))