You entered:

e^4xdx/1+3e^4x

What you mean?

e^4*x*dx/1 + 3*e^4*x

e^(4*x)*dx/1 + 3*e^(4*x)

e^4*x*dx/(1 + 3*e^4*x)

e^4*x*dx*x/(1 + 3*e^4)

e^4*x*dx*4*x/(1 + 3*e)

e^4*x*dx*x/((1 + 3*e)^4)

e^4*x*dx/1 + 3*e^4*x

Integral of e^4xdx/1+3e^4x dx

The solution

You have entered [src]

  1                       
  /                       
 |                        
 |  / 4     1      4  \   
 |  |e *x*1*- + 3*e *x| dx
 |  \       1         /   
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(e^{4} x 1 \cdot 1^{-1} + 3 x e^{4}\right)\, dx$$

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int e^{4} x 1 \cdot 1^{-1}\, dx = e^{4} \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{x^{2} e^{4}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x e^{4}\, dx = 3 e^{4} \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{3 x^{2} e^{4}}{2}$
The result is: $2 x^{2} e^{4}$
Add the constant of integration:

$2 x^{2} e^{4}+ \mathrm{constant}$

The answer is:

$2 x^{2} e^{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                                     
 | / 4     1      4  \             2  4
 | |e *x*1*- + 3*e *x| dx = C + 2*x *e 
 | \       1         /                 
 |                                     
/

$$\int \left(e^{4} x 1 \cdot 1^{-1} + 3 x e^{4}\right)\, dx = C + 2 x^{2} e^{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   4
2*e

$$2 e^{4}$$

   4
2*e

$$2 e^{4}$$

Упростить

Numerical answer [src]

109.196300066288

109.196300066288

The graph

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

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What you mean?

Integral of e^4xdx/1+3e^4x dx

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The graph:

Piecewise:

The solution