What is the integral of (-4)/(x(ln(x))^4) ?

The integral of (-4)/(x(ln(x))^4) is 4/(3ln^3(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (-4)/(x(ln(x))^4)

\int \frac{- 4}{x ( ln ( x ) ) ^{4}} d x

\frac{4}{3 ln ^{3} ( x )} + C

Solution steps

\int \frac{- 4}{x ( ln ( x ) ) ^{4}} d x

Take the constant out:

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

= - 4 \cdot \int \frac{1}{x ( ln ( x ) ) ^{4}} d x

Apply u-substitution

: \int \frac{1}{u ^{4}} d u

= - 4 \cdot \int \frac{1}{u ^{4}} d u

Apply the Power Rule

: - \frac{1}{3 u ^{3}}

= - 4 (- \frac{1}{3 u ^{3}})

Substitute back

u = ln (x)

= - 4 (- \frac{1}{3 ln ^{3} ( x )})

Simplify

- 4 (- \frac{1}{3 ln ^{3} ( x )}) : \frac{4}{3 ln ^{3} ( x )}

= \frac{4}{3 ln ^{3} ( x )}

Add a constant to the solution

= \frac{4}{3 ln ^{3} ( x )} + C

2 x

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

\int \frac{x ^{2}}{5 - x ^{6}} d x

\int \frac{1 + tan ( x )}{1 - cos ( x )} d x

\int e^{- x} sin^{2} (2 x) d x

What is the integral of (-4)/(x(ln(x))^4) ?
The integral of (-4)/(x(ln(x))^4) is 4/(3ln^3(x))+C