What is the integral of 4x(x^2+26000)^{-2/3} ?

The integral of 4x(x^2+26000)^{-2/3} is 6(x^2+26000)^{1/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4x(x^2+26000)^{-2/3}

\int 4 x (x^{2} + 26000)^{- \frac{2}{3}} d x

6 (x^{2} + 26000)^{\frac{1}{3}} + C

Solution steps

\int 4 x (x^{2} + 26000)^{- \frac{2}{3}} d x

Take the constant out:

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

= 4 \cdot \int x (x^{2} + 26000)^{- \frac{2}{3}} d x

Apply u-substitution

: \int \frac{1}{2 u ^{\frac{2}{3}}} d u

= 4 \cdot \int \frac{1}{2 u ^{\frac{2}{3}}} d u

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{\frac{2}{3}}} d u

Apply the Power Rule

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

= 4 \cdot \frac{1}{2} \cdot 3 u^{\frac{1}{3}}

Substitute back

u = x^{2} + 26000

= 4 \cdot \frac{1}{2} \cdot 3 (x^{2} + 26000)^{\frac{1}{3}}

Simplify

4 \cdot \frac{1}{2} \cdot 3 (x^{2} + 26000)^{\frac{1}{3}} : 6 (x^{2} + 26000)^{\frac{1}{3}}

= 6 (x^{2} + 26000)^{\frac{1}{3}}

Add a constant to the solution

= 6 (x^{2} + 26000)^{\frac{1}{3}} + C

f (x) = (x - 4) (3 - x)^{3}

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

\frac{d}{d x} (\frac{2 cos ( x )}{x + 1})

x \to 0 + lim (x)

y^{^{'}} + y = e^{x} sin (e^{x})

What is the integral of 4x(x^2+26000)^{-2/3} ?
The integral of 4x(x^2+26000)^{-2/3} is 6(x^2+26000)^{1/3}+C