What is the integral of 1/((x(ln(x))^3)) ?

The integral of 1/((x(ln(x))^3)) is -1/(2ln^2(x))+C

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integral of 1/((x(ln(x))^3))

\int \frac{1}{( x ( ln ( x ) ) ^{3} )} d x

- \frac{1}{2 ln ^{2} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = ln (x)

= - \frac{1}{2 ln ^{2} ( x )}

Add a constant to the solution

= - \frac{1}{2 ln ^{2} ( x )} + C

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What is the integral of 1/((x(ln(x))^3)) ?
The integral of 1/((x(ln(x))^3)) is -1/(2ln^2(x))+C