What is the integral of ((ln(x))^4)/x ?

The integral of ((ln(x))^4)/x is (ln^5(x))/5+C

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integral of ((ln(x))^4)/x

\int \frac{( ln ( x ) ) ^{4}}{x} d x

\frac{ln ^{5} ( x )}{5} + C

Solution steps

\int \frac{( ln ( x ) ) ^{4}}{x} d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = ln (x)

= \frac{ln ^{5} ( x )}{5}

Add a constant to the solution

= \frac{ln ^{5} ( x )}{5} + C

\int_{1}^{e} x^{2} ln (x) d x

\frac{y ^{4}}{8} + \frac{1}{4 y ^{2}}

5 y^{^{''}} + 26 y = 0

e^{x^{2} + 9 x + 7}

n = 2 \sum \infty 2 n ln (n)

What is the integral of ((ln(x))^4)/x ?
The integral of ((ln(x))^4)/x is (ln^5(x))/5+C