What is the integral of ((ln(x))^8)/x ?

The integral of ((ln(x))^8)/x is (ln^9(x))/9+C

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integral of ((ln(x))^8)/x

\int \frac{( ln ( x ) ) ^{8}}{x} d x

\frac{ln ^{9} ( x )}{9} + C

Solution steps

\int \frac{( ln ( x ) ) ^{8}}{x} d x

Apply u-substitution

: \int u^{8} d u

= \int u^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= \frac{u ^{9}}{9}

Substitute back

u = ln (x)

= \frac{ln ^{9} ( x )}{9}

Add a constant to the solution

= \frac{ln ^{9} ( x )}{9} + C

\int (x^{2} + x + 1) sin (x) d x

x \to - 1 lim (1 + x)

\frac{d}{d x} (\frac{- 12 x}{( x ^{2} + 3 ) ^{2}})

2 x^{2} - 6 x + 3

\frac{\partial}{\partial x} (arccos (x y))

What is the integral of ((ln(x))^8)/x ?
The integral of ((ln(x))^8)/x is (ln^9(x))/9+C