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Integral of d{x}:
Integral of 1/(1+x^5)
Integral of 3*exp(-3*x)
Integral of 2*x/(1+x)
Integral of xe^-1
Identical expressions
three *e^(4x)
3 multiply by e to the power of (4x)
three multiply by e to the power of (4x)
3*e(4x)
3*e4x
3e^(4x)
3e(4x)
3e4x
3e^4x
3*e^(4x)dx

Solving integrals/ 3*e^(4x)

Integral of 3*e^(4x) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     4*x   
 |  3*E    dx
 |           
/            
0

$$\int\limits_{0}^{1} 3 e^{4 x}\, dx$$

Integral(3*E^(4*x), (x, 0, 1))

Detail solution

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

$\int 3 e^{4 x}\, dx = 3 \int e^{4 x}\, dx$
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:
    
    $\text{False}$
    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:
  
  $\frac{e^{4 x}}{4}$
So, the result is: $\frac{3 e^{4 x}}{4}$
Add the constant of integration:

$\frac{3 e^{4 x}}{4}+ \mathrm{constant}$

The answer is:

$\frac{3 e^{4 x}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                    4*x
 |    4*x          3*e   
 | 3*E    dx = C + ------
 |                   4   
/

$$\int 3 e^{4 x}\, dx = C + \frac{3 e^{4 x}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         4
  3   3*e 
- - + ----
  4    4

$$- \frac{3}{4} + \frac{3 e^{4}}{4}$$

=

         4
  3   3*e 
- - + ----
  4    4

$$- \frac{3}{4} + \frac{3 e^{4}}{4}$$

-3/4 + 3*exp(4)/4

Numerical answer [src]

40.1986125248582

40.1986125248582

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