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

y^{^{'}} = y (y + 1) x

\int \frac{1 + ln ( x )}{x ln ( x )} d x

\frac{d}{d x} (3 sin^{2} (x) cos (2 x))

\frac{\partial}{\partial x} ((\frac{x}{x - y})^{\frac{1}{3}})

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

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