Integral of (x+1)*(x-3) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  (x + 1)*(x - 3) dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(x - 3\right) \left(x + 1\right)\, dx$$

Integral((x + 1)*(x - 3), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x - 3\right) \left(x + 1\right) = x^{2} - 2 x - 3$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x\right)\, dx = - 2 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-3\right)\, dx = - 3 x$
The result is: $\frac{x^{3}}{3} - x^{2} - 3 x$
Now simplify:

$\frac{x \left(x^{2} - 3 x - 9\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 3 x - 9\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 3 x - 9\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     3
 |                           2         x 
 | (x + 1)*(x - 3) dx = C - x  - 3*x + --
 |                                     3 
/

$$\int \left(x - 3\right) \left(x + 1\right)\, dx = C + \frac{x^{3}}{3} - x^{2} - 3 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-11/3

$$- \frac{11}{3}$$

-11/3

$$- \frac{11}{3}$$

-11/3

Numerical answer [src]

-3.66666666666667

-3.66666666666667

The graph

Use the examples entering the upper and lower limits of integration.

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x+1)*(x-3) dx

Limits of integration:

The graph:

Piecewise:

The solution