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Integral of d{x}:
Integral of xln(x)
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Integral of x*dx/(x+1)
Integral of e^2x
Identical expressions
(five - four x^ three)*e^(5x-x^4)
(5 minus 4x cubed ) multiply by e to the power of (5x minus x to the power of 4)
(five minus four x to the power of three) multiply by e to the power of (5x minus x to the power of 4)
(5-4x3)*e(5x-x4)
5-4x3*e5x-x4
(5-4x³)*e^(5x-x⁴)
(5-4x to the power of 3)*e to the power of (5x-x to the power of 4)
(5-4x^3)e^(5x-x^4)
(5-4x3)e(5x-x4)
5-4x3e5x-x4
5-4x^3e^5x-x^4
(5-4x^3)*e^(5x-x^4)dx
Similar expressions
(5+4x^3)*e^(5x-x^4)
(5-4x^3)*e^(5x+x^4)

Solving integrals/ (5-4x^3)*e^(5x-x^4)

Integral of (5-4x^3)*e^(5x-x^4) dx

The solution

You have entered [src]

  1                        
  /                        
 |                         
 |                     4   
 |  /       3\  5*x - x    
 |  \5 - 4*x /*e         dx
 |                         
/                          
0

$$\int\limits_{0}^{1} \left(- 4 x^{3} + 5\right) e^{- x^{4} + 5 x}\, dx$$

Simplify

Detail solution

Rewrite the integrand:

$\left(5 - 4 x^{3}\right) e^{- x^{4} + 5 x} = - 4 x^{3} e^{5 x} e^{- x^{4}} + 5 e^{5 x} e^{- x^{4}}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 x^{3} e^{5 x} e^{- x^{4}}\right)\, dx = - 4 \int x^{3} e^{5 x} e^{- x^{4}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\int x^{3} e^{5 x} e^{- x^{4}}\, dx$
  So, the result is: $- 4 \int x^{3} e^{5 x} e^{- x^{4}}\, dx$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 e^{5 x} e^{- x^{4}}\, dx = 5 \int e^{5 x} e^{- x^{4}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\int e^{5 x} e^{- x^{4}}\, dx$
  So, the result is: $5 \int e^{5 x} e^{- x^{4}}\, dx$
The result is: $5 \int e^{5 x} e^{- x^{4}}\, dx - 4 \int x^{3} e^{5 x} e^{- x^{4}}\, dx$
Add the constant of integration:

$5 \int e^{5 x} e^{- x^{4}}\, dx - 4 \int x^{3} e^{5 x} e^{- x^{4}}\, dx+ \mathrm{constant}$

The answer is:

$5 \int e^{5 x} e^{- x^{4}}\, dx - 4 \int x^{3} e^{5 x} e^{- x^{4}}\, dx+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  /                      /            
 |                                  |                      |             
 |                    4             |       4              |    4        
 | /       3\  5*x - x              |  3  -x   5*x         |  -x   5*x   
 | \5 - 4*x /*e         dx = C - 4* | x *e   *e    dx + 5* | e   *e    dx
 |                                  |                      |             
/                                  /                      /

$$e^{5\,x-x^4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      4
-1 + e

$$e^4-1$$

      4
-1 + e

$$-1 + e^{4}$$

Simplify

Numerical answer [src]

53.5981500331442

53.5981500331442

The graph

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

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Similar expressions

Integral of (5-4x^3)*e^(5x-x^4) dx

Limits of integration:

The graph:

Piecewise:

The solution