What is the integral from 5 to 25 of 1/(x(ln(x))^9) ?

The integral from 5 to 25 of 1/(x(ln(x))^9) is (255)/(2048ln^8(5))

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integral from 5 to 25 of 1/(x(ln(x))^9)

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{9}} d x

\frac{255}{2048 ln ^{8} ( 5 )}

Solution steps

\int_{5}^{25} \frac{1}{x ( ln ( x ) ) ^{9}} d x

Simplify

= \int_{5}^{25} \frac{1}{x ln ^{9} ( x )} d x

Apply u-substitution

: \int_{l n (5)}^{2 l n (5)} \frac{1}{u ^{9}} d u

= \int_{l n (5)}^{2 l n (5)} \frac{1}{u ^{9}} d u

Apply the Power Rule

: [- \frac{1}{8 u ^{8}}]_{l n (5)}^{2 l n (5)}

= [- \frac{1}{8 u ^{8}}]_{l n (5)}^{2 l n (5)}

Compute the boundaries:

\frac{255}{2048 ln ^{8} ( 5 )}

= \frac{255}{2048 ln ^{8} ( 5 )}

\int_{0}^{5} \frac{1}{1 - x ^{2}} d x

\int_{0}^{\frac{1}{2}} x arctan (2 x) d x

\int_{2}^{5} ln (x) + sin (x) + 8 d x

\int_{\frac{y}{n}}^{1} n (1 - x)^{n - 1} d x

What is the integral from 5 to 25 of 1/(x(ln(x))^9) ?
The integral from 5 to 25 of 1/(x(ln(x))^9) is (255)/(2048ln^8(5))