What is the integral from 2 to 4 of 1/(x(ln(x))^9) ?

The integral from 2 to 4 of 1/(x(ln(x))^9) is (255)/(2048ln^8(2))

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integral from 2 to 4 of 1/(x(ln(x))^9)

\int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{9}} d x

\frac{255}{2048 ln ^{8} ( 2 )}

Decimal

2.33671 \dots

Solution steps

\int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{9}} d x

Simplify

= \int_{2}^{4} \frac{1}{x ln ^{9} ( x )} d x

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{255}{2048 ln ^{8} ( 2 )}

= \frac{255}{2048 ln ^{8} ( 2 )}

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What is the integral from 2 to 4 of 1/(x(ln(x))^9) ?
The integral from 2 to 4 of 1/(x(ln(x))^9) is (255)/(2048ln^8(2))