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Identical expressions
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x3+2x2+x
(x³+2x²+x)
(x to the power of 3+2x to the power of 2+x)
x^3+2x^2+x
(x^3+2x^2+x)dx
Similar expressions
x^4/(x^3+2*x^2+x+2)
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Solving integrals/ (x^3+2x^2+x)

Integral of (x^3+2x^2+x) dx

The solution

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

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

Integral(x^3 + 2*x^2 + x, (x, 0, 1))

Detail solution

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

$\frac{x^{2} \cdot \left(3 x^{2} + 8 x + 6\right)}{12}$
Add the constant of integration:

$\frac{x^{2} \cdot \left(3 x^{2} + 8 x + 6\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \cdot \left(3 x^{2} + 8 x + 6\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{x^4}\over{4}}+{{2\,x^3}\over{3}}+{{x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

17
--
12

$${{17}\over{12}}$$

17
--
12

$$\frac{17}{12}$$

Simplify

Numerical answer [src]

1.41666666666667

1.41666666666667

The graph

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

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Integral of (x^3+2x^2+x) dx

Limits of integration:

The graph:

Piecewise:

The solution