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

The integral of ((ln(z))^3)/z is (ln^4(z))/4+C

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

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

\frac{ln ^{4} ( z )}{4} + C

Solution steps

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

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = ln (z)

= \frac{ln ^{4} ( z )}{4}

Add a constant to the solution

= \frac{ln ^{4} ( z )}{4} + C

x \to 0 lim (\frac{1}{4 x} - \frac{1}{( e ^{4 x} - 1 )})

\int \frac{1}{x ^{\frac{11}{5}}} d x

\frac{\partial}{\partial x} (tan (9 + 2 x^{2} y^{3} z^{2}))

\frac{\partial}{\partial x} (ln (z))

x \to 0 lim (1 - \frac{tan ( k x )}{x})

What is the integral of ((ln(z))^3)/z ?
The integral of ((ln(z))^3)/z is (ln^4(z))/4+C