Mister Exam

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Integral of exp(y)
Derivative of:
x^2+2x-3
Equation:
x^2+2x-3
Canonical form:
x^2+2x-3
Identical expressions
x^ two +2x- three
x squared plus 2x minus 3
x to the power of two plus 2x minus three
x2+2x-3
x²+2x-3
x to the power of 2+2x-3
x^2+2x-3dx
Similar expressions
x^2-2x-3
(4/x^2)+2*x-3*x^2
x^2+2x+3

Solving integrals/ x^2+2x-3

Integral of x^2+2x-3 dx

The solution

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

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

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

$\frac{x \left(x^{2} + 3 x - 9\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 3 x - 9\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 3 x - 9\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

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

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+2x-3 dx

Limits of integration:

The graph:

Piecewise:

The solution