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Integral of d{x}:
Integral of x×e^x
Integral of e^(x*(-4))
Integral of x^2e^x
Integral of (x*x)*exp(-x/2)
Graphing y =:
-x^2+4*x-1
Factor squared:
-x^2+4*x-1
Identical expressions
-x^ two + four *x- one
minus x squared plus 4 multiply by x minus 1
minus x to the power of two plus four multiply by x minus one
-x2+4*x-1
-x²+4*x-1
-x to the power of 2+4*x-1
-x^2+4x-1
-x2+4x-1
-x^2+4*x-1dx
Similar expressions
-x^2+4*x+1
x^2+4*x-1
-x^2-4*x-1

Integral of -x^2+4*x-1 dx

The solution

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

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

Integral(-x^2 + 4*x - 1, (x, 1, 4))

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:
    
    $\int 4 x\, dx = 4 \int x\, dx$
    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:
  
  $\int \left(-1\right)\, dx = - x$
The result is: $- \frac{x^{3}}{3} + 2 x^{2} - x$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                       
 |                                       3
 | /   2          \                 2   x 
 | \- x  + 4*x - 1/ dx = C - x + 2*x  - --
 |                                      3 
/

$$\int \left(\left(- x^{2} + 4 x\right) - 1\right)\, dx = C - \frac{x^{3}}{3} + 2 x^{2} - x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$6$$

Numerical answer [src]

6.0

6.0

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

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Identical expressions

Similar expressions

Integral of -x^2+4*x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution