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Solving integrals/ e^(x/y)

Integral of e^(x/y) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let u=xyu = \frac{x}{y}.

    Then let du=dxydu = \frac{dx}{y} and substitute duydu y:

    ∫yeu du\int y e^{u}\, du

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

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

      1. The integral of the exponential function is itself.

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

      So, the result is: yeuy e^{u}

    Now substitute uu back in:

    yexyy e^{\frac{x}{y}}

  2. Add the constant of integration:

    yexy+constanty e^{\frac{x}{y}}+ \mathrm{constant}

The answer is:

yexy+constanty e^{\frac{x}{y}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                
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 |  x             x
 |  -             -
 |  y             y
 | E  dx = C + y*e 
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∫exy dx=C+yexy\int e^{\frac{x}{y}}\, dx = C + y e^{\frac{x}{y}}
Simplify
The answer [src] 
        1
        -
        y
-y + y*e
ye1y−yy e^{\frac{1}{y}} - y 
=
= 
        1
        -
        y
-y + y*e
ye1y−yy e^{\frac{1}{y}} - y 
-y + y*exp(1/y)

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

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