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Equation:
x^2+3x+1
Identical expressions
x^ two +3x+ one
x squared plus 3x plus 1
x to the power of two plus 3x plus one
x2+3x+1
x²+3x+1
x to the power of 2+3x+1
x^2+3x+1dx
Similar expressions
x^2-3x+1
x^2+3x-1

Solving integrals/ x^2+3x+1

Integral of x^2+3x+1 dx

The solution

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

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

Integral(x^2 + 3*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 $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x\, dx = 3 \int x\, dx$
    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: $\frac{3 x^{2}}{2}$
  The result is: $\frac{x^{3}}{3} + \frac{3 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{3}}{3} + \frac{3 x^{2}}{2} + x$
Now simplify:

$\frac{x \left(2 x^{2} + 9 x + 6\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} + 9 x + 6\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} + 9 x + 6\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

17/6

$$\frac{17}{6}$$

17/6

$$\frac{17}{6}$$

17/6

Numerical answer [src]

2.83333333333333

2.83333333333333

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^2+3x+1 dx

Limits of integration:

The graph:

Piecewise:

The solution