What is the integral of 1/(xln^8(x)) ?

The integral of 1/(xln^8(x)) is -1/(7ln^7(x))+C

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integral of 1/(xln^8(x))

\int \frac{1}{x ln ^{8} ( x )} d x

- \frac{1}{7 ln ^{7} ( x )} + C

Solution steps

\int \frac{1}{x ln ^{8} ( x )} d x

Apply u-substitution

: \int \frac{1}{u ^{8}} d u

= \int \frac{1}{u ^{8}} d u

Apply the Power Rule

: - \frac{1}{7 u ^{7}}

= - \frac{1}{7 u ^{7}}

Substitute back

u = ln (x)

= - \frac{1}{7 ln ^{7} ( x )}

Add a constant to the solution

= - \frac{1}{7 ln ^{7} ( x )} + C

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What is the integral of 1/(xln^8(x)) ?
The integral of 1/(xln^8(x)) is -1/(7ln^7(x))+C