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Integral of d{x}:
Integral of x^3*e^(x^4)
Integral of x*e^(4*x)
Integral of 1/(4+x^2)
Integral of x/sqrt(1+x^2)
Derivative of:
3*exp(3*x)
Identical expressions
three *exp(three *x)
3 multiply by exponent of (3 multiply by x)
three multiply by exponent of (three multiply by x)
3exp(3x)
3exp3x
3*exp(3*x)dx
Similar expressions
(1/3)*exp(3x)2
-x^3*(exp(3*x^4))*(2*x^4+3)
2*x+3*exp(3*x+2*y)-2*(y-x)*exp((y-x)^2)-1

Solving integrals/ 3*exp(3*x)

Integral of 3exp(3x) dx

The solution

You have entered [src]

  0          
  /          
 |           
 |     3*x   
 |  3*e    dx
 |           
/            
-oo

$$\int\limits_{-\infty}^{0} 3 e^{3 x}\, dx$$

Integral(3*exp(3*x), (x, -oo, 0))

Detail solution

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

$\int 3 e^{3 x}\, dx = 3 \int e^{3 x}\, dx$
1. Let $u = 3 x$ .
  
  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:
  
  $\frac{e^{3 x}}{3}$
So, the result is: $e^{3 x}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                    
 |                     
 |    3*x           3*x
 | 3*e    dx = C + e   
 |                     
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

=

$$1$$

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