Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/(x^2+3)
Integral of x*e^(x^2)
Integral of xexp(-x)
Integral of xtanx
x*e^(x^2)
Limit of the function:
x*e^(x^2)
Derivative of:
x*e^(x^2)
Identical expressions
x*e^(x^ two)
x multiply by e to the power of (x squared )
x multiply by e to the power of (x to the power of two)
x*e(x2)
x*ex2
x*e^(x²)
x*e to the power of (x to the power of 2)
xe^(x^2)
xe(x2)
xex2
xe^x^2
x*e^(x^2)dx
Similar expressions
pi(sqrt(x)e^x)^2
xe^x^2(x^2+1)^2×dx
x*(e^(x^2))
2x*e^x^2-1
xe^(x^(2))

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

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

The solution

You have entered [src]

  1           
  /           
 |            
 |     / 2\   
 |     \x /   
 |  x*E     dx
 |            
/             
0

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

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

Detail solution

Let $u = x^{2}$ .

Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :

$\int \frac{e^{u}}{2}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $\frac{e^{u}}{2}$
Now substitute $u$ back in:

$\frac{e^{x^{2}}}{2}$
Add the constant of integration:

$\frac{e^{x^{2}}}{2}+ \mathrm{constant}$

The answer is:

$\frac{e^{x^{2}}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                   / 2\
 |    / 2\           \x /
 |    \x /          e    
 | x*E     dx = C + -----
 |                    2  
/

$$\int e^{x^{2}} x\, dx = C + \frac{e^{x^{2}}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1   E
- - + -
  2   2

$$- \frac{1}{2} + \frac{e}{2}$$

  1   E
- - + -
  2   2

$$- \frac{1}{2} + \frac{e}{2}$$

-1/2 + E/2

Numerical answer [src]

0.859140914229523

0.859140914229523

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution