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

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

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

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

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

Solution steps

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

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 (x)

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

Add a constant to the solution

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

\int sin (2 x - \frac{π}{4}) d x

x \to 1 lim (1)

y^{^{'}} = \frac{x ^{2} + 1}{3 y ^{2}}

\int \frac{1}{x ^{2} - 7} d x

- 4 y^{^{''}} + 16 y = 0, y (1) = 2, y^{^{'}} (2) = 1

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