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Identical expressions
exp(3x+ five)
exponent of (3x plus 5)
exponent of (3x plus five)
exp3x+5
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Similar expressions
exp(3x-5)

Integral of exp(3x+5) dx

The solution

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  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

Let $u = 3 x + 5$ .

Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :

$\int \frac{e^{u}}{3}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $\frac{e^{u}}{3}$
Now substitute $u$ back in:

$\frac{e^{3 x + 5}}{3}$
Now simplify:

$\frac{e^{3 x + 5}}{3}$
Add the constant of integration:

$\frac{e^{3 x + 5}}{3}+ \mathrm{constant}$

The answer is:

$\frac{e^{3 x + 5}}{3}+ \mathrm{constant}$

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    8
  e    e 
- -- + --
  3    3

$$- \frac{e^{5}}{3} + \frac{e^{8}}{3}$$

   5    8
  e    e 
- -- + --
  3    3

$$- \frac{e^{5}}{3} + \frac{e^{8}}{3}$$

-exp(5)/3 + exp(8)/3

Numerical answer [src]

944.181609313051

944.181609313051

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

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Identical expressions

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Integral of exp(3x+5) dx

Limits of integration:

The graph:

Piecewise:

The solution