Mister Exam

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Integral of d{x}:
Integral of e^(-x)
Integral of -sin(x)
Integral of cos(x/2)
Integral of x-2
Identical expressions
e^(8x- fifteen)
e to the power of (8x minus 15)
e to the power of (8x minus fifteen)
e(8x-15)
e8x-15
e^8x-15
e^(8x-15)dx
Similar expressions
e^(8x+15)

Integral of e^(8x-15) dx

The solution

You have entered [src]

  1             
  /             
 |              
 |   8*x - 15   
 |  E         dx
 |              
/               
0

$$\int\limits_{0}^{1} e^{8 x - 15}\, dx$$

Integral(E^(8*x - 15), (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = 8 x - 15$ .
  
  Then let $du = 8 dx$ and substitute $\frac{du}{8}$ :
  
  $\int \frac{e^{u}}{8}\, du$
  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: $\frac{e^{u}}{8}$
  Now substitute $u$ back in:
  
  $\frac{e^{8 x - 15}}{8}$
Method #2
1. Rewrite the integrand:
  
  $e^{8 x - 15} = \frac{e^{8 x}}{e^{15}}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{e^{8 x}}{e^{15}}\, dx = \frac{\int e^{8 x}\, dx}{e^{15}}$
  1. Let $u = 8 x$ .
    
    Then let $du = 8 dx$ and substitute $\frac{du}{8}$ :
    
    $\int \frac{e^{u}}{8}\, du$
    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: $\frac{e^{u}}{8}$
    Now substitute $u$ back in:
    
    $\frac{e^{8 x}}{8}$
  So, the result is: $\frac{e^{8 x}}{8 e^{15}}$
Method #3
1. Rewrite the integrand:
  
  $e^{8 x - 15} = \frac{e^{8 x}}{e^{15}}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{e^{8 x}}{e^{15}}\, dx = \frac{\int e^{8 x}\, dx}{e^{15}}$
  1. Let $u = 8 x$ .
    
    Then let $du = 8 dx$ and substitute $\frac{du}{8}$ :
    
    $\int \frac{e^{u}}{8}\, du$
    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: $\frac{e^{u}}{8}$
    Now substitute $u$ back in:
    
    $\frac{e^{8 x}}{8}$
  So, the result is: $\frac{e^{8 x}}{8 e^{15}}$
Now simplify:

$\frac{e^{8 x - 15}}{8}$
Add the constant of integration:

$\frac{e^{8 x - 15}}{8}+ \mathrm{constant}$

The answer is:

$\frac{e^{8 x - 15}}{8}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                     8*x - 15
 |  8*x - 15          e        
 | E         dx = C + ---------
 |                        8    
/

$$\int e^{8 x - 15}\, dx = C + \frac{e^{8 x - 15}}{8}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   -15    -7
  e      e  
- ---- + ---
   8      8

$$- \frac{1}{8 e^{15}} + \frac{1}{8 e^{7}}$$

   -15    -7
  e      e  
- ---- + ---
   8      8

$$- \frac{1}{8 e^{15}} + \frac{1}{8 e^{7}}$$

-exp(-15)/8 + exp(-7)/8

Numerical answer [src]

0.000113947007904252

0.000113947007904252

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

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Identical expressions

Similar expressions

Integral of e^(8x-15) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2

Method #3