What is the integral of ((ln(x))^9)/x ?

The integral of ((ln(x))^9)/x is (ln^{10}(x))/(10)+C

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integral of ((ln(x))^9)/x

\int \frac{( ln ( x ) ) ^{9}}{x} d x

\frac{ln ^{10} ( x )}{10} + C

Solution steps

\int \frac{( ln ( x ) ) ^{9}}{x} d x

Apply u-substitution

: \int u^{9} d u

= \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= \frac{u ^{10}}{10}

Substitute back

u = ln (x)

= \frac{ln ^{10} ( x )}{10}

Add a constant to the solution

= \frac{ln ^{10} ( x )}{10} + C

x \to 1 - lim (e^{\frac{3}{( 1 - x )}})

\int_{0}^{1} (6 x - 9 x^{2}) 5 x d x

- 3 y^{^{'}} + \frac{2 y}{x} = x^{2} y^{4}

\frac{d}{d x} (3 2 x + 3)

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

What is the integral of ((ln(x))^9)/x ?
The integral of ((ln(x))^9)/x is (ln^{10}(x))/(10)+C