Mister Exam

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Integral of d{x}:
Integral of x^(-1/2)
Integral of 1/sqrt(1+u^2)
Integral of x*2^(-x)
Integral of x*sin2x
Factor polynomial:
x^2-8*x+15
Graphing y =:
x^2-8*x+15
Identical expressions
x^ two - eight *x+ fifteen
x squared minus 8 multiply by x plus 15
x to the power of two minus eight multiply by x plus fifteen
x2-8*x+15
x²-8*x+15
x to the power of 2-8*x+15
x^2-8x+15
x2-8x+15
x^2-8*x+15dx
Similar expressions
x^2+8*x+15
x^2-8*x-15

Integral of x^2-8*x+15 dx

The solution

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  5                   
  /                   
 |                    
 |  / 2           \   
 |  \x  - 8*x + 15/ dx
 |                    
/                     
3

$$\int\limits_{3}^{5} \left(\left(x^{2} - 8 x\right) + 15\right)\, dx$$

Integral(x^2 - 8*x + 15, (x, 3, 5))

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:
    
    $\int \left(- 8 x\right)\, dx = - 8 \int x\, dx$
    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: $- 4 x^{2}$
  The result is: $\frac{x^{3}}{3} - 4 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 15\, dx = 15 x$
The result is: $\frac{x^{3}}{3} - 4 x^{2} + 15 x$
Now simplify:

$\frac{x \left(x^{2} - 12 x + 45\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 12 x + 45\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 12 x + 45\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         3
 | / 2           \             2          x 
 | \x  - 8*x + 15/ dx = C - 4*x  + 15*x + --
 |                                        3 
/

$$\int \left(\left(x^{2} - 8 x\right) + 15\right)\, dx = C + \frac{x^{3}}{3} - 4 x^{2} + 15 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-4/3

$$- \frac{4}{3}$$

-4/3

$$- \frac{4}{3}$$

-4/3

Numerical answer [src]

-1.33333333333333

-1.33333333333333

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

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Identical expressions

Similar expressions

Integral of x^2-8*x+15 dx

Limits of integration:

The graph:

Piecewise:

The solution