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Identical expressions
four hundred and eighty-two . six * twenty-five *(one -exp(-x/ ninety-four . five))
482.6 multiply by 25 multiply by (1 minus exponent of ( minus x divide by 94.5))
four hundred and eighty minus two . six multiply by twenty minus five multiply by (one minus exponent of ( minus x divide by ninety minus four . five))
482.625(1-exp(-x/94.5))
482.6251-exp-x/94.5
482.6*25*(1-exp(-x divide by 94.5))
482.6*25*(1-exp(-x/94.5))dx
Similar expressions
482.6*25*(1-exp(x/94.5))
482.6*25*(1+exp(-x/94.5))

Solving integrals/ 482.6*25*(1-exp(-x/94.5))

Integral of 482.625(1-exp(-x/94.5)) dx

The solution

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 50                        
  /                        
 |                         
 |          /      -x  \   
 |          |     -----|   
 |  2413*25 |     189/2|   
 |  -------*\1 - e     / dx
 |     5                   
 |                         
/                          
-50

$$\int\limits_{-50}^{50} \frac{25 \cdot 2413}{5} \left(1 - e^{\frac{\left(-1\right) x}{\frac{189}{2}}}\right)\, dx$$

Integral((2413*25/5)*(1 - exp((-x)/(189/2))), (x, -50, 50))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{25 \cdot 2413}{5} \left(1 - e^{\frac{\left(-1\right) x}{\frac{189}{2}}}\right)\, dx = 12065 \int \left(1 - e^{\frac{\left(-1\right) x}{\frac{189}{2}}}\right)\, dx$
1. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, dx = x$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- e^{\frac{\left(-1\right) x}{\frac{189}{2}}}\right)\, dx = - \int e^{\frac{\left(-1\right) x}{\frac{189}{2}}}\, dx$
    1. Let $u = \frac{\left(-1\right) x}{\frac{189}{2}}$ .
      
      Then let $du = - \frac{2 dx}{189}$ and substitute $- \frac{189 du}{2}$ :
      
      $\int \left(- \frac{189 e^{u}}{2}\right)\, du$
      1. The integral of a constant times a function is the constant times the integral of the function:
        
        $\text{False}$
        
        The integral of the exponential function is itself.
        
        $\int e^{u}\, du = e^{u}$
        
        So, the result is: $- \frac{189 e^{u}}{2}$
      Now substitute $u$ back in:
      
      $- \frac{189 e^{\frac{\left(-1\right) x}{\frac{189}{2}}}}{2}$
    So, the result is: $\frac{189 e^{\frac{\left(-1\right) x}{\frac{189}{2}}}}{2}$
  The result is: $x + \frac{189 e^{\frac{\left(-1\right) x}{\frac{189}{2}}}}{2}$
So, the result is: $12065 x + \frac{2280285 e^{\frac{\left(-1\right) x}{\frac{189}{2}}}}{2}$
Now simplify:

$12065 x + \frac{2280285 e^{- \frac{2 x}{189}}}{2}$
Add the constant of integration:

$12065 x + \frac{2280285 e^{- \frac{2 x}{189}}}{2}+ \mathrm{constant}$

The answer is:

$12065 x + \frac{2280285 e^{- \frac{2 x}{189}}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                      
 |                                                   -x  
 |         /      -x  \                             -----
 |         |     -----|                             189/2
 | 2413*25 |     189/2|                    2280285*e     
 | -------*\1 - e     / dx = C + 12065*x + --------------
 |    5                                          2       
 |                                                       
/

$$\int \frac{25 \cdot 2413}{5} \left(1 - e^{\frac{\left(-1\right) x}{\frac{189}{2}}}\right)\, dx = C + 12065 x + \frac{2280285 e^{\frac{\left(-1\right) x}{\frac{189}{2}}}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                   100            -100 
                   ---            -----
                   189             189 
          2280285*e      2280285*e     
1206500 - ------------ + --------------
               2               2

$$- \frac{2280285 e^{\frac{100}{189}}}{2} + \frac{2280285}{2 e^{\frac{100}{189}}} + 1206500$$

                   100            -100 
                   ---            -----
                   189             189 
          2280285*e      2280285*e     
1206500 - ------------ + --------------
               2               2

$$- \frac{2280285 e^{\frac{100}{189}}}{2} + \frac{2280285}{2 e^{\frac{100}{189}}} + 1206500$$

1206500 - 2280285*exp(100/189)/2 + 2280285*exp(-100/189)/2

Numerical answer [src]

-57085.9731535679

-57085.9731535679

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

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Integral of 482.625(1-exp(-x/94.5)) dx

Limits of integration:

The graph:

Piecewise:

The solution

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Integral of 482.6*25*(1-exp(-x/94.5)) dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of 482.625(1-exp(-x/94.5)) dx