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e^(x+1)
Solving integrals/ e^(x+1)

Integral of e^(x+1) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |   x + 1   
 |  E      dx
 |           
/            
0
∫01ex+1 dx\int\limits_{0}^{1} e^{x + 1}\, dx 
Integral(E^(x + 1), (x, 0, 1))
Detail solution

  1. There are multiple ways to do this integral.

    Method #1

    1. Let u=x+1u = x + 1.

      Then let du=dxdu = dx and substitute dudu:

      ∫eu du\int e^{u}\, du

      1. The integral of the exponential function is itself.

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

      Now substitute uu back in:

      ex+1e^{x + 1}

    Method #2

    1. Rewrite the integrand:

      ex+1=eexe^{x + 1} = e e^{x}

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

      ∫eex dx=e∫ex dx\int e e^{x}\, dx = e \int e^{x}\, dx

      1. The integral of the exponential function is itself.

        ∫ex dx=ex\int e^{x}\, dx = e^{x}

      So, the result is: eexe e^{x}

  2. Now simplify:

    ex+1e^{x + 1}

  3. Add the constant of integration:

    ex+1+constante^{x + 1}+ \mathrm{constant}

The answer is:

ex+1+constante^{x + 1}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                       
 |  x + 1           x + 1
 | E      dx = C + e     
 |                       
/
∫ex+1 dx=C+ex+1\int e^{x + 1}\, dx = C + e^{x + 1}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
      2
-E + e
−e+e2- e + e^{2} 
=
= 
      2
-E + e
−e+e2- e + e^{2} 
-E + exp(2)
Numerical answer [src] 
4.6707742704716
4.6707742704716
The graph
Integral of e^(x+1) dx

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

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