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

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

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

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

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

Solution steps

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

y^{^{'}} = \frac{( 2 y + 3 ) ^{2}}{( 4 x + 5 ) ^{2}}

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

\frac{d}{d x} (\frac{e ^{x} - 2}{( 1 - e ^{- x} ) ^{2}})

\int \frac{( 5 x ^{2} )}{1 - 5 x ^{3}} d x

x \to 0 + lim (sin (\frac{π}{x}))

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