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

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

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

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

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

Solution steps

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

\frac{\partial}{\partial x} (tan (3 x - 5 y))

\frac{\partial}{\partial x} (y^{2} - 1)

\int \frac{x}{x - 1} d x

n = 0 \sum \infty (\frac{7}{18})^{n}

sec (x) \frac{d y}{d x} + y = 1

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