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Integral of cosecx
Identical expressions
x^2e^(-x^ four + four)
x squared e to the power of ( minus x to the power of 4 plus 4)
x squared e to the power of ( minus x to the power of four plus four)
x2e(-x4+4)
x2e-x4+4
x²e^(-x⁴+4)
x to the power of 2e to the power of (-x to the power of 4+4)
x^2e^-x^4+4
x^2e^(-x^4+4)dx
Similar expressions
x^2e^(x^4+4)
x^2e^(-x^4-4)
What you mean?
x^2*e^(-x^4 + 4)
x^((2*e)^(-x^4 + 4))
x^((2*e)^(-x^4 + 4))

You entered:

x^2e^(-x^4+4)

What you mean?

x^2*e^(-x^4 + 4)

x^((2*e)^(-x^4 + 4))

x^((2*e)^(-x^4 + 4))

Integral of x^2e^(-x^4+4) dx

The solution

You have entered [src]

  1                
  /                
 |                 
 |         4       
 |   2  - x  + 4   
 |  x *e         dx
 |                 
/                  
0

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

Integral(x^2*E^(-x^4 + 4), (x, 0, 1))

Detail solution

Rewrite the integrand:

$x^{2} e^{4 - x^{4}} = x^{2} e^{4} e^{- x^{4}}$
The integral of a constant times a function is the constant times the integral of the function:

$\int x^{2} e^{4} e^{- x^{4}}\, dx = e^{4} \int x^{2} e^{- x^{4}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{3 \Gamma\left(\frac{3}{4}\right) \gamma\left(\frac{3}{4}, x^{4}\right)}{16 \Gamma\left(\frac{7}{4}\right)}$
So, the result is: $\frac{3 e^{4} \Gamma\left(\frac{3}{4}\right) \gamma\left(\frac{3}{4}, x^{4}\right)}{16 \Gamma\left(\frac{7}{4}\right)}$
Now simplify:

$\frac{e^{4} \gamma\left(\frac{3}{4}, x^{4}\right)}{4}$
Add the constant of integration:

$\frac{e^{4} \gamma\left(\frac{3}{4}, x^{4}\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{e^{4} \gamma\left(\frac{3}{4}, x^{4}\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                         
 |                                                          
 |        4                 4                      /      4\
 |  2  - x  + 4          3*e *Gamma(3/4)*lowergamma\3/4, x /
 | x *e         dx = C + -----------------------------------
 |                                  16*Gamma(7/4)           
/

$$-{{e^4\,\Gamma\left({{3}\over{4}} , x^4\right)\,x}\over{4\,\left| x \right| }}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   4                  4           
  e *Gamma(3/4, 1)   e *Gamma(3/4)
- ---------------- + -------------
         4                 4

$${{e^4\,\Gamma\left({{3}\over{4}}\right)}\over{4}}-{{e^4\,\Gamma \left({{3}\over{4}} , 1\right)}\over{4}}$$

   4                  4           
  e *Gamma(3/4, 1)   e *Gamma(3/4)
- ---------------- + -------------
         4                 4

$$- \frac{e^{4} \Gamma\left(\frac{3}{4}, 1\right)}{4} + \frac{e^{4} \Gamma\left(\frac{3}{4}\right)}{4}$$

Упростить

Numerical answer [src]

12.3771807034838

12.3771807034838

The graph

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

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Identical expressions

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You entered:

What you mean?

Integral of x^2e^(-x^4+4) dx

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The graph:

Piecewise:

The solution