Mister Exam

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Integral of d{x}:
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Integral of ex^2
Integral of -e^x
Integral of (1+2x^2)/(x^2(1+x^2))
Graphing y =:
x^2+x-1
Canonical form:
x^2+x-1
Factor squared:
x^2+x-1
Identical expressions
x^ two +x- one
x squared plus x minus 1
x to the power of two plus x minus one
x2+x-1
x²+x-1
x to the power of 2+x-1
x^2+x-1dx
Similar expressions
x^2+x+1
x^2-x-1

Solving integrals/ x^2+x-1

Integral of x^2+x-1 dx

The solution

You have entered [src]

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

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

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

$x \left(\frac{x^{2}}{3} + \frac{x}{2} - 1\right)$
Add the constant of integration:

$x \left(\frac{x^{2}}{3} + \frac{x}{2} - 1\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{2}}{3} + \frac{x}{2} - 1\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/6

$$- \frac{1}{6}$$

-1/6

$$- \frac{1}{6}$$

-1/6

Numerical answer [src]

-0.166666666666667

-0.166666666666667

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+x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution