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Identical expressions
four *x*exp(x^ two)
4 multiply by x multiply by exponent of (x squared )
four multiply by x multiply by exponent of (x to the power of two)
4*x*exp(x2)
4*x*expx2
4*x*exp(x²)
4*x*exp(x to the power of 2)
4xexp(x^2)
4xexp(x2)
4xexpx2
4xexpx^2
4*x*exp(x^2)dx

Solving integrals/ 4*x*exp(x^2)

Integral of 4xexp(x^2) dx

The solution

You have entered [src]

  1             
  /             
 |              
 |       / 2\   
 |       \x /   
 |  4*x*e     dx
 |              
/               
0

$$\int\limits_{0}^{1} 4 x e^{x^{2}}\, dx$$

Integral((4*x)*exp(x^2), (x, 0, 1))

Detail solution

Let $u = x^{2}$ .

Then let $du = 2 x dx$ and substitute $2 du$ :

$\int 2 e^{u}\, du$
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: $2 e^{u}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                          
 |                           
 |      / 2\             / 2\
 |      \x /             \x /
 | 4*x*e     dx = C + 2*e    
 |                           
/

$$\int 4 x e^{x^{2}}\, dx = C + 2 e^{x^{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2 + 2*E

$$-2 + 2 e$$

-2 + 2*E

$$-2 + 2 e$$

-2 + 2*E

Numerical answer [src]

3.43656365691809

3.43656365691809

The graph

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

Other calculators

How to use it?

Identical expressions

Integral of 4xexp(x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Integral of 4*x*exp(x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of 4xexp(x^2) dx