What is the integral of 5/(16x(ln(x))^8) ?

The integral of 5/(16x(ln(x))^8) is -5/(112ln^7(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 5/(16x(ln(x))^8)

\int \frac{5}{16 x ( ln ( x ) ) ^{8}} d x

- \frac{5}{112 ln ^{7} ( x )} + C

Solution steps

\int \frac{5}{16 x ( ln ( x ) ) ^{8}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{5}{16} \cdot \int \frac{1}{x ( ln ( x ) ) ^{8}} d x

Apply u-substitution

= \frac{5}{16} \cdot \int \frac{1}{u ^{8}} d u

Apply the Power Rule

= \frac{5}{16} (- \frac{1}{7 u ^{7}})

Substitute back

u = ln (x)

= \frac{5}{16} (- \frac{1}{7 ln ^{7} ( x )})

Simplify

\frac{5}{16} (- \frac{1}{7 ln ^{7} ( x )}) : - \frac{5}{112 ln ^{7} ( x )}

= - \frac{5}{112 ln ^{7} ( x )}

Add a constant to the solution

= - \frac{5}{112 ln ^{7} ( x )} + C

What is the integral of 5/(16x(ln(x))^8) ?
The integral of 5/(16x(ln(x))^8) is -5/(112ln^7(x))+C