What is the integral of 3/(zln^3(z)) ?

The integral of 3/(zln^3(z)) is -3/(2ln^2(z))+C

integral of 3/(zln^3(z))

\int \frac{3}{z ln ^{3} ( z )} d z

- \frac{3}{2 ln ^{2} ( z )} + C

Solution steps

\int \frac{3}{z ln ^{3} ( z )} d z

Take the constant out:

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

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

Apply u-substitution

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

Apply the Power Rule

= 3 (- \frac{1}{2 u ^{2}})

Substitute back

u = ln (z)

= 3 (- \frac{1}{2 ln ^{2} ( z )})

Simplify

3 (- \frac{1}{2 ln ^{2} ( z )}) : - \frac{3}{2 ln ^{2} ( z )}

= - \frac{3}{2 ln ^{2} ( z )}

Add a constant to the solution

= - \frac{3}{2 ln ^{2} ( z )} + C

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