What is the integral of ((ln(x))^5)/x ?

The integral of ((ln(x))^5)/x is (ln^6(x))/6+C

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integral of ((ln(x))^5)/x

\int \frac{( ln ( x ) ) ^{5}}{x} d x

\frac{ln ^{6} ( x )}{6} + C

Solution steps

\int \frac{( ln ( x ) ) ^{5}}{x} d x

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = ln (x)

= \frac{ln ^{6} ( x )}{6}

Add a constant to the solution

= \frac{ln ^{6} ( x )}{6} + C

\frac{d}{d x} (5 sec (5 x) tan (5 x))

\int_{0}^{0.5} 8 y^{2} d y

\frac{5}{t ^{2}}

\int \frac{3}{9 x ^{2} + 6 x + 1} d x

\int \frac{x ^{2} + x + 1}{x ^{2} + 1} d x

What is the integral of ((ln(x))^5)/x ?
The integral of ((ln(x))^5)/x is (ln^6(x))/6+C