What is the integral of 1/(\sqrt[3]{(4-x)^2)} ?

The integral of 1/(\sqrt[3]{(4-x)^2)} is -3\sqrt[3]{4-x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(\sqrt[3]{(4-x)^2)}

\int \frac{1}{3 ( 4 - x ) ^{2}} d x

- 3 3 4 - x + C

Solution steps

\int \frac{1}{3 ( 4 - x ) ^{2}} d x

3 (4 - x)^{2} = (4 - x)^{\frac{2}{3}},

assuming

(4 - x) \geq 0

= \int \frac{1}{( 4 - x ) ^{\frac{2}{3}}} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = 4 - x

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

Apply radical rule:

a^{\frac{1}{n}} = n a

= - 3 3 4 - x

Add a constant to the solution

= - 3 3 4 - x + C

\int e^{x} (1 + 4 e^{x})^{5} d x

\int sec (x) tan (x) - 8 e^{x} d x

\int sin^{2} (\frac{1}{x}) d x

\int cot^{5} (3 - 2 x) csc^{3} (3 - 2 x) d x

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

What is the integral of 1/(\sqrt[3]{(4-x)^2)} ?
The integral of 1/(\sqrt[3]{(4-x)^2)} is -3\sqrt[3]{4-x}+C