What is the integral of 1/(x(ln(x))^{15)} ?

The integral of 1/(x(ln(x))^{15)} is -1/(14ln^{14)(x)}+C

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integral of 1/(x(ln(x))^{15)}

\int \frac{1}{x ( ln ( x ) ) ^{15}} d x

- \frac{1}{14 ln ^{14} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{15}} d x

Apply u-substitution

: \int \frac{1}{u ^{15}} d u

= \int \frac{1}{u ^{15}} d u

Apply the Power Rule

: - \frac{1}{14 u ^{14}}

= - \frac{1}{14 u ^{14}}

Substitute back

u = ln (x)

= - \frac{1}{14 ln ^{14} ( x )}

Add a constant to the solution

= - \frac{1}{14 ln ^{14} ( x )} + C

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What is the integral of 1/(x(ln(x))^{15)} ?
The integral of 1/(x(ln(x))^{15)} is -1/(14ln^{14)(x)}+C