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Identical expressions
(two x^2+5x- one)dx
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(two x squared plus 5x minus one)dx
(2x2+5x-1)dx
2x2+5x-1dx
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Similar expressions
(2x^2-5x-1)dx
(2x^2+5x+1)dx

Integral of (2x^2+5x-1)dx dx

The solution

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  1                    
  /                    
 |                     
 |  /   2          \   
 |  \2*x  + 5*x - 1/ dx
 |                     
/                      
0

$$\int\limits_{0}^{1} \left(\left(2 x^{2} + 5 x\right) - 1\right)\, dx$$

Integral(2*x^2 + 5*x - 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  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 a constant times a function is the constant times the integral of the function:
    
    $\int 5 x\, dx = 5 \int x\, dx$
    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: $\frac{5 x^{2}}{2}$
  The result is: $\frac{2 x^{3}}{3} + \frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $\frac{2 x^{3}}{3} + \frac{5 x^{2}}{2} - x$
Now simplify:

$\frac{x \left(4 x^{2} + 15 x - 6\right)}{6}$
Add the constant of integration:

$\frac{x \left(4 x^{2} + 15 x - 6\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(4 x^{2} + 15 x - 6\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                  3      2
 | /   2          \              2*x    5*x 
 | \2*x  + 5*x - 1/ dx = C - x + ---- + ----
 |                                3      2  
/

$$\int \left(\left(2 x^{2} + 5 x\right) - 1\right)\, dx = C + \frac{2 x^{3}}{3} + \frac{5 x^{2}}{2} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

13/6

$$\frac{13}{6}$$

13/6

$$\frac{13}{6}$$

13/6

Numerical answer [src]

2.16666666666667

2.16666666666667

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

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Integral of (2x^2+5x-1)dx dx

Limits of integration:

The graph:

Piecewise:

The solution