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

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

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

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

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

Solution steps

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

2 y^{^{'}} - y = e^{\frac{t}{3}}

f (x) = 5 ln (x)

\int_{0}^{2} - 2 x^{3} x^{2} + 4 d x

x \to 3 - lim (\frac{∣ x - 3 ∣}{x + 3})

3 t - t^{2} (0)

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