What is the integral of 1/(x(ln(x))^{17)} ?

The integral of 1/(x(ln(x))^{17)} is -1/(16ln^{16)(x)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(x(ln(x))^{17)}

\int \frac{1}{x ( ln ( x ) ) ^{17}} d x

- \frac{1}{16 ln ^{16} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{17}} d x

Apply u-substitution

: \int \frac{1}{u ^{17}} d u

= \int \frac{1}{u ^{17}} d u

Apply the Power Rule

: - \frac{1}{16 u ^{16}}

= - \frac{1}{16 u ^{16}}

Substitute back

u = ln (x)

= - \frac{1}{16 ln ^{16} ( x )}

Add a constant to the solution

= - \frac{1}{16 ln ^{16} ( x )} + C

\int \frac{1}{x 5 + 1} d x

\int \frac{1}{1 - \frac{x ^{2}}{81}} d x

\int \frac{5}{( 2 x + 1 ) ( x - 2 )} d x

\int (x^{2} + 1) (x^{3} + 3 x - 1)^{5} d x

\int \frac{1}{4 x ^{2} - 11 x + 2} d x

What is the integral of 1/(x(ln(x))^{17)} ?
The integral of 1/(x(ln(x))^{17)} is -1/(16ln^{16)(x)}+C