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Identical expressions
((x^ three -x^ two / two)+x+ one)dx
((x cubed minus x squared divide by 2) plus x plus 1)dx
((x to the power of three minus x to the power of two divide by two) plus x plus one)dx
((x3-x2/2)+x+1)dx
x3-x2/2+x+1dx
((x³-x²/2)+x+1)dx
((x to the power of 3-x to the power of 2/2)+x+1)dx
x^3-x^2/2+x+1dx
((x^3-x^2 divide by 2)+x+1)dx
Similar expressions
((x^3-x^2/2)+x-1)dx
((x^3-x^2/2)-x+1)dx
((x^3+x^2/2)+x+1)dx

Solving integrals/ ((x^3-x^2/2)+x+1)dx

Integral of ((x^3-x^2/2)+x+1)dx dx

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |  /      2        \   
 |  | 3   x         |   
 |  |x  - -- + x + 1| dx
 |  \     2         /   
 |                      
/                       
0

$$\int\limits_{0}^{1} \left(\left(x + \left(x^{3} - \frac{x^{2}}{2}\right)\right) + 1\right)\, dx$$

Integral(x^3 - x^2/2 + x + 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  1. 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 a constant times a function is the constant times the integral of the function:
      
      $\int \left(- \frac{x^{2}}{2}\right)\, dx = - \frac{\int x^{2}\, dx}{2}$
      1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
        
        $\int x^{2}\, dx = \frac{x^{3}}{3}$
      So, the result is: $- \frac{x^{3}}{6}$
    The result is: $\frac{x^{4}}{4} - \frac{x^{3}}{6}$
  The result is: $\frac{x^{4}}{4} - \frac{x^{3}}{6} + \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{4}}{4} - \frac{x^{3}}{6} + \frac{x^{2}}{2} + x$
Now simplify:

$x \left(\frac{x^{3}}{4} - \frac{x^{2}}{6} + \frac{x}{2} + 1\right)$
Add the constant of integration:

$x \left(\frac{x^{3}}{4} - \frac{x^{2}}{6} + \frac{x}{2} + 1\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{3}}{4} - \frac{x^{2}}{6} + \frac{x}{2} + 1\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                            
 | /      2        \               2    3    4
 | | 3   x         |              x    x    x 
 | |x  - -- + x + 1| dx = C + x + -- - -- + --
 | \     2         /              2    6    4 
 |                                            
/

$$\int \left(\left(x + \left(x^{3} - \frac{x^{2}}{2}\right)\right) + 1\right)\, dx = C + \frac{x^{4}}{4} - \frac{x^{3}}{6} + \frac{x^{2}}{2} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

19
--
12

$$\frac{19}{12}$$

19
--
12

$$\frac{19}{12}$$

19/12

Numerical answer [src]

1.58333333333333

1.58333333333333

The graph

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

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Integral of ((x^3-x^2/2)+x+1)dx dx

Limits of integration:

The graph:

Piecewise:

The solution