What is the integral of ((ln(x))^{15})/x ?

The integral of ((ln(x))^{15})/x is (ln^{16}(x))/(16)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((ln(x))^{15})/x

\int \frac{( ln ( x ) ) ^{15}}{x} d x

\frac{ln ^{16} ( x )}{16} + C

Solution steps

\int \frac{( ln ( x ) ) ^{15}}{x} d x

Apply u-substitution

: \int u^{15} d u

= \int u^{15} d u

Apply the Power Rule

: \frac{u ^{16}}{16}

= \frac{u ^{16}}{16}

Substitute back

u = ln (x)

= \frac{ln ^{16} ( x )}{16}

Add a constant to the solution

= \frac{ln ^{16} ( x )}{16} + C

y = x^{3} - 2 x^{2} + 5

n \to \infty lim (k = 1 \sum n (4 + \frac{3 k}{n})^{2} (\frac{3}{n}))

12 - 4 e^{x}

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

\int \frac{5 x + 3}{x ^{2} + 4} d x

What is the integral of ((ln(x))^{15})/x ?
The integral of ((ln(x))^{15})/x is (ln^{16}(x))/(16)+C