Integral of 2xe^x² dx

The solution

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

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

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

Detail solution

Let $u = x^{2}$ .

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

$\int e^{u}\, du$
1. The integral of the exponential function is itself.
  
  $\int e^{u}\, du = e^{u}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1 + E

$$-1 + e$$

-1 + E

$$-1 + e$$

-1 + E

Numerical answer [src]

1.71828182845905

1.71828182845905

The graph

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

Other calculators

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Identical expressions

Integral of 2xe^x² dx

Limits of integration:

The graph:

Piecewise:

The solution