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Solving integrals/ exp(3x-5)

Integral of exp(3x-5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |   3*x - 5   
 |  e        dx
 |             
/              
0
$$\int\limits_{0}^{1} e^{3 x - 5}\, dx$$ 
Integral(exp(3*x - 5), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          
 |                    3*x - 5
 |  3*x - 5          e       
 | e        dx = C + --------
 |                      3    
/
$$\int e^{3 x - 5}\, dx = C + \frac{e^{3 x - 5}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   -5    -2
  e     e  
- --- + ---
   3     3
$$- \frac{1}{3 e^{5}} + \frac{1}{3 e^{2}}$$ 
=
= 
   -5    -2
  e     e  
- --- + ---
   3     3
$$- \frac{1}{3 e^{5}} + \frac{1}{3 e^{2}}$$ 
-exp(-5)/3 + exp(-2)/3
Numerical answer [src] 
0.0428657787458424
0.0428657787458424

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

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