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Integral of 15e^(5x)-3 dx

Limits of integration:

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The graph:

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The solution

You have entered [src]
  1                 
  /                 
 |                  
 |  /    5*x    \   
 |  \15*E    - 3/ dx
 |                  
/                   
0                   
$$\int\limits_{0}^{1} \left(15 e^{5 x} - 3\right)\, dx$$
Integral(15*E^(5*x) - 3, (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

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

      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:

      So, the result is:

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                   
 |                                    
 | /    5*x    \                   5*x
 | \15*E    - 3/ dx = C - 3*x + 3*e   
 |                                    
/                                     
$$\int \left(15 e^{5 x} - 3\right)\, dx = C - 3 x + 3 e^{5 x}$$
The graph
The answer [src]
        5
-6 + 3*e 
$$-6 + 3 e^{5}$$
=
=
        5
-6 + 3*e 
$$-6 + 3 e^{5}$$
-6 + 3*exp(5)
Numerical answer [src]
439.23947730773
439.23947730773

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

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