What is the integral of ((ln(x))^{12})/x ?

The integral of ((ln(x))^{12})/x is (ln^{13}(x))/(13)+C

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integral of ((ln(x))^{12})/x

\int \frac{( ln ( x ) ) ^{12}}{x} d x

\frac{ln ^{13} ( x )}{13} + C

Solution steps

\int \frac{( ln ( x ) ) ^{12}}{x} d x

Apply u-substitution

: \int u^{12} d u

= \int u^{12} d u

Apply the Power Rule

: \frac{u ^{13}}{13}

= \frac{u ^{13}}{13}

Substitute back

u = ln (x)

= \frac{ln ^{13} ( x )}{13}

Add a constant to the solution

= \frac{ln ^{13} ( x )}{13} + C

\frac{d}{d x} (12 e^{\frac{x}{2}})

\int \frac{e ^{x} ( x ln ( x ) + 1 )}{x} d x

\frac{3 x + 8}{x ^{2}}

\frac{( 3 s + 1 )}{s + 2}

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

What is the integral of ((ln(x))^{12})/x ?
The integral of ((ln(x))^{12})/x is (ln^{13}(x))/(13)+C