Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of (x+1)e^(2x)
Integral of (x+1)/(2x²+3x-4)
Integral of e^(1/x)/x^4
Integral of e^(1/(x-1))/((x)^(1/3))
Identical expressions
e^(4x+ one)
e to the power of (4x plus 1)
e to the power of (4x plus one)
e(4x+1)
e4x+1
e^4x+1
e^(4x+1)dx
Similar expressions
e^(4x-1)

Solving integrals/ e^(4x+1)

Integral of e^(4x+1) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |   4*x + 1   
 |  E        dx
 |             
/              
0

$$\int\limits_{0}^{1} e^{4 x + 1}\, dx$$

Integral(E^(4*x + 1), (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = 4 x + 1$ .
  
  Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :
  
  $\int \frac{e^{u}}{4}\, du$
  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: $\frac{e^{u}}{4}$
  Now substitute $u$ back in:
  
  $\frac{e^{4 x + 1}}{4}$
Method #2
1. Rewrite the integrand:
  
  $e^{4 x + 1} = e e^{4 x}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int e e^{4 x}\, dx = e \int e^{4 x}\, dx$
  1. Let $u = 4 x$ .
    
    Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :
    
    $\int \frac{e^{u}}{4}\, du$
    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: $\frac{e^{u}}{4}$
    Now substitute $u$ back in:
    
    $\frac{e^{4 x}}{4}$
  So, the result is: $\frac{e e^{4 x}}{4}$
Method #3
1. Rewrite the integrand:
  
  $e^{4 x + 1} = e e^{4 x}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int e e^{4 x}\, dx = e \int e^{4 x}\, dx$
  1. Let $u = 4 x$ .
    
    Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :
    
    $\int \frac{e^{u}}{4}\, du$
    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: $\frac{e^{u}}{4}$
    Now substitute $u$ back in:
    
    $\frac{e^{4 x}}{4}$
  So, the result is: $\frac{e e^{4 x}}{4}$
Now simplify:

$\frac{e^{4 x + 1}}{4}$
Add the constant of integration:

$\frac{e^{4 x + 1}}{4}+ \mathrm{constant}$

The answer is:

$\frac{e^{4 x + 1}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                    4*x + 1
 |  4*x + 1          e       
 | E        dx = C + --------
 |                      4    
/

$$\int e^{4 x + 1}\, dx = C + \frac{e^{4 x + 1}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

       5
  E   e 
- - + --
  4   4

$$- \frac{e}{4} + \frac{e^{5}}{4}$$

       5
  E   e 
- - + --
  4   4

$$- \frac{e}{4} + \frac{e^{5}}{4}$$

-E/4 + exp(5)/4

Numerical answer [src]

36.4237193185294

36.4237193185294

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of e^(4x+1) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2

Method #3