What is the integral from 7 to 49 of 1/(x(ln(x))^8) ?

The integral from 7 to 49 of 1/(x(ln(x))^8) is (127)/(896ln^7(7))

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integral from 7 to 49 of 1/(x(ln(x))^8)

\int_{7}^{49} \frac{1}{x ( ln ( x ) ) ^{8}} d x

\frac{127}{896 ln ^{7} ( 7 )}

Decimal

0.00134 \dots

Solution steps

\int_{7}^{49} \frac{1}{x ( ln ( x ) ) ^{8}} d x

Apply u-substitution

: \int_{l n (7)}^{2 l n (7)} \frac{1}{u ^{8}} d u

= \int_{l n (7)}^{2 l n (7)} \frac{1}{u ^{8}} d u

Apply the Power Rule

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

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

Compute the boundaries:

\frac{127}{896 ln ^{7} ( 7 )}

= \frac{127}{896 ln ^{7} ( 7 )}

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What is the integral from 7 to 49 of 1/(x(ln(x))^8) ?
The integral from 7 to 49 of 1/(x(ln(x))^8) is (127)/(896ln^7(7))