en

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-4)

Solution

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

Solution

\frac{x ^{4}}{4} - \frac{4 x ^{3}}{3} + C

Solution steps

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

Expand

x^{2} (x - 4) : x^{3} - 4 x^{2}

= \int x^{3} - 4 x^{2} 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 x^{3} d x - \int 4 x^{2} d x

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

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

= \frac{x ^{4}}{4} - \frac{4 x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{4 x ^{3}}{3} + C

Popular Examples

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

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

integral of 0.5Q

\int 0.5 Q d Q

integral of (e^{3x})/(x^3)

\int \frac{e ^{3 x}}{x ^{3}} d x

integral of xsin(2x)cos(x)

\int x sin (2 x) cos (x) d x

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

\int \frac{e ^{2 x}}{3 + e ^{4 x}} d x

Frequently Asked Questions (FAQ)

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