What is the integral from 3 to 9 of 1/(x(ln(x))^6) ?

The integral from 3 to 9 of 1/(x(ln(x))^6) is (31)/(160ln^5(3))

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integral from 3 to 9 of 1/(x(ln(x))^6)

\int_{3}^{9} \frac{1}{x ( ln ( x ) ) ^{6}} d x

\frac{31}{160 ln ^{5} ( 3 )}

Decimal

0.12106 \dots

Solution steps

\int_{3}^{9} \frac{1}{x ( ln ( x ) ) ^{6}} d x

Apply u-substitution

: \int_{l n (3)}^{2 l n (3)} \frac{1}{u ^{6}} d u

= \int_{l n (3)}^{2 l n (3)} \frac{1}{u ^{6}} d u

Apply the Power Rule

: [- \frac{1}{5 u ^{5}}]_{l n (3)}^{2 l n (3)}

= [- \frac{1}{5 u ^{5}}]_{l n (3)}^{2 l n (3)}

Compute the boundaries:

\frac{31}{160 ln ^{5} ( 3 )}

= \frac{31}{160 ln ^{5} ( 3 )}

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What is the integral from 3 to 9 of 1/(x(ln(x))^6) ?
The integral from 3 to 9 of 1/(x(ln(x))^6) is (31)/(160ln^5(3))