What is the integral of 1/(x(ln(x))^6) ?

The integral of 1/(x(ln(x))^6) is -1/(5ln^5(x))+C

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integral of 1/(x(ln(x))^6)

\int \frac{1}{x ( ln ( x ) ) ^{6}} d x

- \frac{1}{5 ln ^{5} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{6}} d x

Apply u-substitution

: \int \frac{1}{u ^{6}} d u

= \int \frac{1}{u ^{6}} d u

Apply the Power Rule

: - \frac{1}{5 u ^{5}}

= - \frac{1}{5 u ^{5}}

Substitute back

u = ln (x)

= - \frac{1}{5 ln ^{5} ( x )}

Add a constant to the solution

= - \frac{1}{5 ln ^{5} ( x )} + C

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What is the integral of 1/(x(ln(x))^6) ?
The integral of 1/(x(ln(x))^6) is -1/(5ln^5(x))+C