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Integral of d{x}:
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Integral of dx/(5-2*x)
Graphing y =:
x^3+3x-1
Identical expressions
x^ three +3x- one
x cubed plus 3x minus 1
x to the power of three plus 3x minus one
x3+3x-1
x³+3x-1
x to the power of 3+3x-1
x^3+3x-1dx
Similar expressions
x^3+3x+1
x^3-3x-1

Solving integrals/ x^3+3x-1

Integral of x^3+3x-1 dx

The solution

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

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

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

29/4

$${{29}\over{4}}$$

29/4

$$\frac{29}{4}$$

Simplify

Numerical answer [src]

7.25

7.25

The graph

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

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Integral of x^3+3x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution