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Integral of e^(x/y) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
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01exydx\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:

    yeudu\int y e^{u}\, du

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

      eudu=yeudu\int e^{u}\, du = y \int e^{u}\, du

      1. The integral of the exponential function is itself.

        eudu=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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exydx=C+yexy\int e^{\frac{x}{y}}\, dx = C + y e^{\frac{x}{y}}
The answer [src]
        1
        -
        y
-y + y*e 
ye1yyy e^{\frac{1}{y}} - y
=
=
        1
        -
        y
-y + y*e 
ye1yyy e^{\frac{1}{y}} - y
-y + y*exp(1/y)

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