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

The integral of x^2(3+x)^2 is 3x^3+(3x^4)/2+(x^5)/5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

3 x^{3} + \frac{3 x ^{4}}{2} + \frac{x ^{5}}{5} + C

Solution steps

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

Expand

x^{2} (3 + x)^{2} : 9 x^{2} + 6 x^{3} + x^{4}

= \int 9 x^{2} + 6 x^{3} + x^{4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 9 x^{2} d x + \int 6 x^{3} d x + \int x^{4} d x

\int 9 x^{2} d x = 3 x^{3}

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

\int x^{4} d x = \frac{x ^{5}}{5}

= 3 x^{3} + \frac{3 x ^{4}}{2} + \frac{x ^{5}}{5}

Add a constant to the solution

= 3 x^{3} + \frac{3 x ^{4}}{2} + \frac{x ^{5}}{5} + C

What is the integral of x^2(3+x)^2 ?
The integral of x^2(3+x)^2 is 3x^3+(3x^4)/2+(x^5)/5+C