What is the integral of (20000)/((x+100)^3) ?

The integral of (20000)/((x+100)^3) is -(10000)/((x+100)^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (20000)/((x+100)^3)

\int \frac{20000}{( x + 100 ) ^{3}} d x

- \frac{10000}{( x + 100 ) ^{2}} + C

Solution steps

\int \frac{20000}{( x + 100 ) ^{3}} d x

Take the constant out:

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

= 20000 \cdot \int \frac{1}{( x + 100 ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= 20000 \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= 20000 (- \frac{1}{2 u ^{2}})

Substitute back

u = x + 100

= 20000 (- \frac{1}{2 ( x + 100 ) ^{2}})

Simplify

20000 (- \frac{1}{2 ( x + 100 ) ^{2}}) : - \frac{10000}{( x + 100 ) ^{2}}

= - \frac{10000}{( x + 100 ) ^{2}}

Add a constant to the solution

= - \frac{10000}{( x + 100 ) ^{2}} + C

\int 8 x e^{x^{2}} d x

\int (- 1) d x

\frac{\partial}{\partial z} (\frac{x y}{z})

\frac{\partial}{\partial x} (7 - x^{4} + 2 x^{2} - y^{2})

\frac{d y}{d x} + 5 y = e^{x} y^{- 2}

What is the integral of (20000)/((x+100)^3) ?
The integral of (20000)/((x+100)^3) is -(10000)/((x+100)^2)+C