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Integral of d{x}:
Integral of x^2*e^(-x)
Integral of e^u
Integral of e^(x/2)
Integral of √(1-x²)
Canonical form:
-x^2-4x+5
Graphing y =:
-x^2-4x+5
Identical expressions
-x^ two -4x+ five
minus x squared minus 4x plus 5
minus x to the power of two minus 4x plus five
-x2-4x+5
-x²-4x+5
-x to the power of 2-4x+5
-x^2-4x+5dx
Similar expressions
-x^2+4x+5
-x^2-4x-5
x^2-4x+5

Integral of -x^2-4x+5 dx

The solution

You have entered [src]

  1                    
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 |  /   2          \   
 |  \- x  - 4*x + 5/ dx
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/                      
0

$$\int\limits_{0}^{1} \left(\left(- x^{2} - 4 x\right) + 5\right)\, dx$$

Integral(-x^2 - 4*x + 5, (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:
    
    $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
    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: $- \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 4 x\right)\, dx = - 4 \int x\, dx$
    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: $- 2 x^{2}$
  The result is: $- \frac{x^{3}}{3} - 2 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 5\, dx = 5 x$
The result is: $- \frac{x^{3}}{3} - 2 x^{2} + 5 x$
Now simplify:

$\frac{x \left(- x^{2} - 6 x + 15\right)}{3}$
Add the constant of integration:

$\frac{x \left(- x^{2} - 6 x + 15\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- x^{2} - 6 x + 15\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         3
 | /   2          \             2         x 
 | \- x  - 4*x + 5/ dx = C - 2*x  + 5*x - --
 |                                        3 
/

$$\int \left(\left(- x^{2} - 4 x\right) + 5\right)\, dx = C - \frac{x^{3}}{3} - 2 x^{2} + 5 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

8/3

$$\frac{8}{3}$$

8/3

$$\frac{8}{3}$$

8/3

Numerical answer [src]

2.66666666666667

2.66666666666667

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

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Integral of -x^2-4x+5 dx

Limits of integration:

The graph:

Piecewise:

The solution