Mister Exam

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Integral of d{x}:
Integral of x^2*e^x
Integral of arctan(x)
Integral of (ln(x))^2
Integral of x-1
Identical expressions
(x*|x|)/ two
(x multiply by module of x|) divide by 2
(x multiply by module of x|) divide by two
(x|x|)/2
x|x|/2
(x*|x|) divide by 2
(x*|x|)/2dx

Integral of (x*|x|)/2 dx

The solution

You have entered [src]

  1         
  /         
 |          
 |  x*|x|   
 |  ----- dx
 |    2     
 |          
/           
-1

$$\int\limits_{-1}^{1} \frac{x \left|{x}\right|}{2}\, dx$$

Integral((x*|x|)/2, (x, -1, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{x \left|{x}\right|}{2}\, dx = \frac{\int x \left|{x}\right|\, dx}{2}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\int x \left|{x}\right|\, dx$
So, the result is: $\frac{\int x \left|{x}\right|\, dx}{2}$
Add the constant of integration:

$\frac{\int x \left|{x}\right|\, dx}{2}+ \mathrm{constant}$

The answer is:

$\frac{\int x \left|{x}\right|\, dx}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

                    /        
                   |         
  /                | x*|x| dx
 |                 |         
 | x*|x|          /          
 | ----- dx = C + -----------
 |   2                 2     
 |                           
/

$$\int \frac{x \left|{x}\right|}{2}\, dx = C + \frac{\int x \left|{x}\right|\, dx}{2}$$

Simplify

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

Integral of (x*|x|)/2 dx

Limits of integration:

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Piecewise:

The solution