Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*2^(-x)
Integral of ex^2
Integral of (1/x^2)dx
Integral of x*cos(x/2)
Identical expressions
(x- three)*(x- five)
(x minus 3) multiply by (x minus 5)
(x minus three) multiply by (x minus five)
(x-3)(x-5)
x-3x-5
(x-3)*(x-5)dx
Similar expressions
(x-2)(x-3)(x-5)-(4-x^2)/(x-2)
(x+3)*(x-5)
(x-3)*(x+5)

Integral of (x-3)*(x-5) dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  (x - 3)*(x - 5) dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(x - 5\right) \left(x - 3\right)\, dx$$

Integral((x - 3)*(x - 5), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x - 5\right) \left(x - 3\right) = x^{2} - 8 x + 15$
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: $- 4 x^{2}$
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          x 
 | (x - 3)*(x - 5) dx = C - 4*x  + 15*x + --
 |                                        3 
/

$$\int \left(x - 5\right) \left(x - 3\right)\, dx = C + \frac{x^{3}}{3} - 4 x^{2} + 15 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

34/3

$$\frac{34}{3}$$

34/3

$$\frac{34}{3}$$

34/3

Numerical answer [src]

11.3333333333333

11.3333333333333

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x-3)*(x-5) dx

Limits of integration:

The graph:

Piecewise:

The solution