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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

u = x^{2} - 2

= \frac{1}{2} \cdot \frac{( x ^{2} - 2 ) ^{3}}{3}

Simplify

\frac{1}{2} \cdot \frac{( x ^{2} - 2 ) ^{3}}{3} : \frac{1}{6} (x^{2} - 2)^{3}

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

Add a constant to the solution

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

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

\int \frac{1}{x ^{8}} d x

\int \frac{( x ^{2} + 2 )}{2 x} d x

\int sin (x) 1 + cos (x) d x

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