What is the integral of ((ln(x))^{16})/x ?

The integral of ((ln(x))^{16})/x is (ln^{17}(x))/(17)+C

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integral of ((ln(x))^{16})/x

\int \frac{( ln ( x ) ) ^{16}}{x} d x

\frac{ln ^{17} ( x )}{17} + C

Solution steps

\int \frac{( ln ( x ) ) ^{16}}{x} d x

Apply u-substitution

: \int u^{16} d u

= \int u^{16} d u

Apply the Power Rule

: \frac{u ^{17}}{17}

= \frac{u ^{17}}{17}

Substitute back

u = ln (x)

= \frac{ln ^{17} ( x )}{17}

Add a constant to the solution

= \frac{ln ^{17} ( x )}{17} + C

x \to 0 lim (\frac{cos ( x ) - 1}{x})

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\int_{- \infty}^{0} 2^{x} d x

What is the integral of ((ln(x))^{16})/x ?
The integral of ((ln(x))^{16})/x is (ln^{17}(x))/(17)+C