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Similar expressions
(x-1)(x^2-2)
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Solving integrals/ (x+1)(x^2-2)

Integral of (x+1)(x^2-2) dx

The solution

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  0                    
  /                    
 |                     
 |          / 2    \   
 |  (x + 1)*\x  - 2/ dx
 |                     
/                      
-1

$$\int\limits_{-1}^{0} \left(x + 1\right) \left(x^{2} - 2\right)\, dx$$

Integral((x + 1)*(x^2 - 2), (x, -1, 0))

Detail solution

Rewrite the integrand:

$\left(x + 1\right) \left(x^{2} - 2\right) = x^{3} + x^{2} - 2 x - 2$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
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:
  
  $\int \left(-2\right)\, dx = - 2 x$
The result is: $\frac{x^{4}}{4} + \frac{x^{3}}{3} - x^{2} - 2 x$
Now simplify:

$x \left(\frac{x^{3}}{4} + \frac{x^{2}}{3} - x - 2\right)$
Add the constant of integration:

$x \left(\frac{x^{3}}{4} + \frac{x^{2}}{3} - x - 2\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{3}}{4} + \frac{x^{2}}{3} - x - 2\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                       3    4
 |         / 2    \           2         x    x 
 | (x + 1)*\x  - 2/ dx = C - x  - 2*x + -- + --
 |                                      3    4 
/

$$\int \left(x + 1\right) \left(x^{2} - 2\right)\, dx = C + \frac{x^{4}}{4} + \frac{x^{3}}{3} - x^{2} - 2 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-11 
----
 12

$$- \frac{11}{12}$$

-11 
----
 12

$$- \frac{11}{12}$$

-11/12

Numerical answer [src]

-0.916666666666667

-0.916666666666667

The graph

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

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Identical expressions

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Integral of (x+1)(x^2-2) dx

Limits of integration:

The graph:

Piecewise:

The solution