Mister Exam

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

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### The solution

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  1
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|  /    5*x    \
|  \15*E    - 3/ dx
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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:

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

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

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