What is the integral of x(2-x^2)^3 ?

The integral of x(2-x^2)^3 is -1/8 (2-x^2)^4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(2-x^2)^3

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

- \frac{1}{8} (2 - x^{2})^{4} + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = 2 - x^{2}

= - \frac{1}{2} \cdot \frac{( 2 - x ^{2} ) ^{4}}{4}

Simplify

- \frac{1}{2} \cdot \frac{( 2 - x ^{2} ) ^{4}}{4} : - \frac{1}{8} (2 - x^{2})^{4}

= - \frac{1}{8} (2 - x^{2})^{4}

Add a constant to the solution

= - \frac{1}{8} (2 - x^{2})^{4} + C

\int \frac{2 x - 1}{x ^{2} - 1} d x

\int sec^{2} (x) tan^{1} (x) d x

\int \frac{5.4145}{1 + 0.91 x} d x

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

\int \frac{x}{a ^{2} - x ^{2}} d x

What is the integral of x(2-x^2)^3 ?
The integral of x(2-x^2)^3 is -1/8 (2-x^2)^4+C