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Solving integrals/ exp(3x)

Integral of exp(3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo        
  /        
 |         
 |   3*x   
 |  e    dx
 |         
/          
-oo
∫−∞∞e3x dx\int\limits_{-\infty}^{\infty} e^{3 x}\, dx 
Integral(exp(3*x), (x, -oo, oo))
Detail solution

  1. Let u=3xu = 3 x.

    Then let du=3dxdu = 3 dx and substitute du3\frac{du}{3}:

    ∫eu3 du\int \frac{e^{u}}{3}\, du

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

      False\text{False}

      1. The integral of the exponential function is itself.

        ∫eu du=eu\int e^{u}\, du = e^{u}

      So, the result is: eu3\frac{e^{u}}{3}

    Now substitute uu back in:

    e3x3\frac{e^{3 x}}{3}

  2. Add the constant of integration:

    e3x3+constant\frac{e^{3 x}}{3}+ \mathrm{constant}

The answer is:

e3x3+constant\frac{e^{3 x}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                3*x
 |  3*x          e   
 | e    dx = C + ----
 |                3  
/
∫e3x dx=C+e3x3\int e^{3 x}\, dx = C + \frac{e^{3 x}}{3}
Simplify
The graph
-0.010-0.008-0.006-0.004-0.0020.0100.0000.0020.0040.0060.00801
Plot the graph f(x)
The answer [src] 
oo
∞\infty 
=
= 
oo
∞\infty 
oo
Numerical answer [src] 
2.61707303999408e+13000078344468995219
2.61707303999408e+13000078344468995219

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

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