What is the integral of 2/(x(ln(x))^3) ?

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

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integral of 2/(x(ln(x))^3)

\int \frac{2}{x ( ln ( x ) ) ^{3}} d x

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

Solution steps

\int \frac{2}{x ( ln ( x ) ) ^{3}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{1}{x ( ln ( x ) ) ^{3}} d x

Apply u-substitution

= 2 \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

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

Substitute back

u = ln (x)

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

Simplify

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

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

Add a constant to the solution

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

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