Mister Exam

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Identical expressions
(two x^2+x- one)
(2x squared plus x minus 1)
(two x squared plus x minus one)
(2x2+x-1)
2x2+x-1
(2x²+x-1)
(2x to the power of 2+x-1)
2x^2+x-1
(2x^2+x-1)dx
Similar expressions
(2x^2-x-1)
(2x^2+x+1)

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

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

The solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

32/3

$$\frac{32}{3}$$

32/3

$$\frac{32}{3}$$

32/3

Numerical answer [src]

10.6666666666667

10.6666666666667

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

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

Limits of integration:

The graph:

Piecewise:

The solution