What is the integral of ((ln(x))^{11})/x ?

The integral of ((ln(x))^{11})/x is (ln^{12}(x))/(12)+C

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integral of ((ln(x))^{11})/x

\int \frac{( ln ( x ) ) ^{11}}{x} d x

\frac{ln ^{12} ( x )}{12} + C

Solution steps

\int \frac{( ln ( x ) ) ^{11}}{x} d x

Simplify

= \int \frac{ln ^{11} ( x )}{x} d x

Apply u-substitution

: \int u^{11} d u

= \int u^{11} d u

Apply the Power Rule

: \frac{u ^{12}}{12}

= \frac{u ^{12}}{12}

Substitute back

u = ln (x)

= \frac{ln ^{12} ( x )}{12}

Add a constant to the solution

= \frac{ln ^{12} ( x )}{12} + C

(arctan (x))^{^{'}}

\frac{d}{d x} (8 e^{x} + \frac{8}{3 x})

\int \frac{5}{3 x ^{2}} d x

\int \frac{4}{( x + 1 ) ( x + 3 )} d x

x \to \infty lim (\frac{8 ^{x}}{9 ^{x + 1}})

What is the integral of ((ln(x))^{11})/x ?
The integral of ((ln(x))^{11})/x is (ln^{12}(x))/(12)+C