What is the integral of (((ln(x))^7))/x ?

The integral of (((ln(x))^7))/x is (ln^8(x))/8+C

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integral of (((ln(x))^7))/x

\int \frac{( ( ln ( x ) ) ^{7} )}{x} d x

\frac{ln ^{8} ( x )}{8} + C

Solution steps

\int \frac{( ln ( x ) ) ^{7}}{x} d x

Apply u-substitution

: \int u^{7} d u

= \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{u ^{8}}{8}

Substitute back

u = ln (x)

= \frac{ln ^{8} ( x )}{8}

Add a constant to the solution

= \frac{ln ^{8} ( x )}{8} + C

\frac{d}{d x} (- (x + 1)^{- 1})

\frac{d}{d y} (e^{\frac{x}{y}})

x \to 6 lim (- \frac{1}{x - 6})

\frac{d y}{d x} = \frac{x ^{2} + 2 y}{x}

\int (\frac{x + 11}{x - 9}) d x

What is the integral of (((ln(x))^7))/x ?
The integral of (((ln(x))^7))/x is (ln^8(x))/8+C