What is the integral of 1/((1/3 x-8)^5) ?

The integral of 1/((1/3 x-8)^5) is -(243)/(4(x-24)^4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((1/3 x-8)^5)

\int \frac{1}{( \frac{1}{3} x - 8 ) ^{5}} d x

- \frac{243}{4 ( x - 24 ) ^{4}} + C

Solution steps

\int \frac{1}{( \frac{1}{3} x - 8 ) ^{5}} d x

Take the partial fraction of

\frac{1}{( \frac{1}{3} x - 8 ) ^{5}} : \frac{243}{( x - 24 ) ^{5}}

= \int \frac{243}{( x - 24 ) ^{5}} d x

Take the constant out:

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

= 243 \cdot \int \frac{1}{( x - 24 ) ^{5}} d x

Apply u-substitution

: \int \frac{1}{u ^{5}} d u

= 243 \cdot \int \frac{1}{u ^{5}} d u

Apply the Power Rule

: - \frac{1}{4 u ^{4}}

= 243 (- \frac{1}{4 u ^{4}})

Substitute back

u = x - 24

= 243 (- \frac{1}{4 ( x - 24 ) ^{4}})

Simplify

243 (- \frac{1}{4 ( x - 24 ) ^{4}}) : - \frac{243}{4 ( x - 24 ) ^{4}}

= - \frac{243}{4 ( x - 24 ) ^{4}}

Add a constant to the solution

= - \frac{243}{4 ( x - 24 ) ^{4}} + C

\frac{d ^{2}}{d x ^{2}} (3 x^{2} + 4 x)

\frac{\partial}{\partial x} (x e^{3 x y})

n = 1 \sum \infty \frac{5 n}{2 n + 1}

\frac{d}{d x} (18 + x)

\int \frac{3 x + 1}{x ^{2} + 3 x - 10} d x

What is the integral of 1/((1/3 x-8)^5) ?
The integral of 1/((1/3 x-8)^5) is -(243)/(4(x-24)^4)+C