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Identical expressions
6xe^x^ two
6xe to the power of x squared
6xe to the power of x to the power of two
6xex2
6xe^x²
6xe to the power of x to the power of 2
6xe^x^2dx

Solving integrals/ 6xe^x^2

Integral of 6xe^x^2 dx

The solution

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  1             
  /             
 |              
 |       / 2\   
 |       \x /   
 |  6*x*E     dx
 |              
/               
0

$$\int\limits_{0}^{1} e^{x^{2}} \cdot 6 x\, dx$$

Integral((6*x)*E^(x^2), (x, 0, 1))

Detail solution

Let $u = x^{2}$ .

Then let $du = 2 x dx$ and substitute $3 du$ :

$\int 3 e^{u}\, du$
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: $3 e^{u}$
Now substitute $u$ back in:

$3 e^{x^{2}}$
Add the constant of integration:

$3 e^{x^{2}}+ \mathrm{constant}$

The answer is:

$3 e^{x^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                           
 |      / 2\             / 2\
 |      \x /             \x /
 | 6*x*E     dx = C + 3*e    
 |                           
/

$$\int e^{x^{2}} \cdot 6 x\, dx = C + 3 e^{x^{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-3 + 3*E

$$-3 + 3 e$$

-3 + 3*E

$$-3 + 3 e$$

-3 + 3*E

Numerical answer [src]

5.15484548537714

5.15484548537714

The graph

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

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Identical expressions

Integral of 6xe^x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution