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

The integral from 3 to 9 of 1/(x(ln(x))^9) is (255)/(2048ln^8(3))

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

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

\frac{255}{2048 ln ^{8} ( 3 )}

Decimal

0.05867 \dots

Solution steps

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

Simplify

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

Apply u-substitution

= \int_{l n (3)}^{2 l n (3)} \frac{1}{u ^{9}} d u

Apply the Power Rule

= [- \frac{1}{8 u ^{8}}]_{l n (3)}^{2 l n (3)}

Compute the boundaries:

\frac{255}{2048 ln ^{8} ( 3 )}

= \frac{255}{2048 ln ^{8} ( 3 )}

What is the integral from 3 to 9 of 1/(x(ln(x))^9) ?
The integral from 3 to 9 of 1/(x(ln(x))^9) is (255)/(2048ln^8(3))