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

\frac{d}{d x} (2 x y + y^{2})

y = x - x^{2}, (- 1, - 2)

t^{3} sin (3 t)

f^{^{'}} (x) = 5 x + 1

(tan (y))^{^{'}}

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