Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (x*ln(x))/(1+x^2)^2
Integral of x/(x^2+4*x+8)
Integral of x/(sqrt(2x+1)+1)
Integral of x*cos6x
Identical expressions
(two x^ two)/(e^x^2)
(2x squared ) divide by (e to the power of x squared )
(two x to the power of two) divide by (e to the power of x squared )
(2x2)/(ex2)
2x2/ex2
(2x²)/(e^x²)
(2x to the power of 2)/(e to the power of x to the power of 2)
2x^2/e^x^2
(2x^2) divide by (e^x^2)
(2x^2)/(e^x^2)dx

Solving integrals/ (2x^2)/(e^x^2)

Integral of (2x^2)/(e^x^2) dx

The solution

You have entered [src]

  1         
  /         
 |          
 |      2   
 |   2*x    
 |  ----- dx
 |   / 2\   
 |   \x /   
 |  e       
 |          
/           
0

$$\int\limits_{0}^{1} \frac{2 x^{2}}{e^{x^{2}}}\, dx$$

Integral(2*x^2/(E^(x^2)), (x, 0, 1))

Detail solution

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

$\int \frac{2 x^{2}}{e^{x^{2}}}\, dx = 2 \int \frac{x^{2}}{e^{x^{2}}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- \frac{x e^{- x^{2}}}{2} + \frac{\sqrt{\pi} \operatorname{erf}{\left(x \right)}}{4}$
So, the result is: $- x e^{- x^{2}} + \frac{\sqrt{\pi} \operatorname{erf}{\left(x \right)}}{2}$
Add the constant of integration:

$- x e^{- x^{2}} + \frac{\sqrt{\pi} \operatorname{erf}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$- x e^{- x^{2}} + \frac{\sqrt{\pi} \operatorname{erf}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                      
 |     2            ____               2
 |  2*x           \/ pi *erf(x)      -x 
 | ----- dx = C + ------------- - x*e   
 |  / 2\                2               
 |  \x /                                
 | e                                    
 |                                      
/

$$2\,\left({{\sqrt{\pi}\,\mathrm{erf}\left(x\right)}\over{4}}-{{x\,e ^ {- x^2 }}\over{2}}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

          ____       
   -1   \/ pi *erf(1)
- e   + -------------
              2

$${{e^ {- 1 }\,\left(\sqrt{\pi}\,e\,\mathrm{erf}\left(1\right)-2 \right)}\over{2}}$$

          ____       
   -1   \/ pi *erf(1)
- e   + -------------
              2

$$- \frac{1}{e} + \frac{\sqrt{\pi} \operatorname{erf}{\left(1 \right)}}{2}$$

Упростить

Numerical answer [src]

0.378944691640985

0.378944691640985

The graph

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

Other calculators

How to use it?

Identical expressions

Integral of (2x^2)/(e^x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution