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Solving integrals/ exp(4x)

Integral of exp(4x) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
 -oo       
  /        
 |         
 |   4*x   
 |  e    dx
 |         
/          
0
∫0−∞e4x dx\int\limits_{0}^{-\infty} e^{4 x}\, dx 
Integral(exp(4*x), (x, 0, -oo))
Detail solution

  1. Let u=4xu = 4 x.

    Then let du=4dxdu = 4 dx and substitute du4\frac{du}{4}:

    ∫eu4 du\int \frac{e^{u}}{4}\, 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: eu4\frac{e^{u}}{4}

    Now substitute uu back in:

    e4x4\frac{e^{4 x}}{4}

  2. Add the constant of integration:

    e4x4+constant\frac{e^{4 x}}{4}+ \mathrm{constant}

The answer is:

e4x4+constant\frac{e^{4 x}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                4*x
 |  4*x          e   
 | e    dx = C + ----
 |                4  
/
∫e4x dx=C+e4x4\int e^{4 x}\, dx = C + \frac{e^{4 x}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
-1/4
−14- \frac{1}{4} 
=
= 
-1/4
−14- \frac{1}{4} 
-1/4

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

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