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Similar expressions
2x*e^x^2+1

Integral of 2x*e^x^2-1 dx

The solution

You have entered [src]

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

$$\int\limits_{2}^{4} \left(2 x e^{x^{2}} - 1\right)\, dx$$

Integral(2*x*E^(x^2) - 1*1, (x, 2, 4))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 x e^{x^{2}}\, dx = 2 \int x e^{x^{2}}\, dx$
  1. Let $u = e^{x^{2}}$ .
    
    Then let $du = 2 x e^{x^{2}} dx$ and substitute $\frac{du}{2}$ :
    
    $\int \frac{1}{4}\, du$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{1}{2}\, du = \frac{\int 1\, du}{2}$
      1. The integral of a constant is the constant times the variable of integration:
        
        $\int 1\, du = u$
      So, the result is: $\frac{u}{2}$
    Now substitute $u$ back in:
    
    $\frac{e^{x^{2}}}{2}$
  So, the result is: $e^{x^{2}}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(\left(-1\right) 1\right)\, dx = - x$
The result is: $- x + e^{x^{2}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                  
 |                                   
 | /     / 2\    \               / 2\
 | |     \x /    |               \x /
 | \2*x*e     - 1/ dx = C - x + e    
 |                                   
/

$$e^{x^2}-x$$

Simplify

The answer [src]

      4    16
-2 - e  + e

$$e^{16}-e^4-2$$

      4    16
-2 - e  + e

$$- e^{4} - 2 + e^{16}$$

Упростить

Numerical answer [src]

8886053.92235784

8886053.92235784

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

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Integral of 2x*e^x^2-1 dx

Limits of integration:

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Piecewise:

The solution