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How to use it?
Integral of d{x}:
Integral of e^(-3x)
Integral of x^2*dx
Integral of (1-x^2)^(1/2)
Integral of 1÷(1+x^2)
The double integral of:
e^(x/y)
e^(x/y)
Identical expressions
e^(x/y)
e to the power of (x divide by y)
e(x/y)
ex/y
e^x/y
e^(x divide by y)
e^(x/y)dx

Solving integrals/ e^(x/y)

Integral of e^(x/y) dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} e^{\frac{x}{y}}\, dx$$

Integral(E^(x/y), (x, 0, 1))

Detail solution

Let $u = \frac{x}{y}$ .

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

$\int y e^{u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int e^{u}\, du = y \int e^{u}\, du$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $y e^{u}$
Now substitute $u$ back in:

$y e^{\frac{x}{y}}$
Add the constant of integration:

$y e^{\frac{x}{y}}+ \mathrm{constant}$

The answer is:

$y e^{\frac{x}{y}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                
 |                 
 |  x             x
 |  -             -
 |  y             y
 | E  dx = C + y*e 
 |                 
/

$$\int e^{\frac{x}{y}}\, dx = C + y e^{\frac{x}{y}}$$

Simplify

The answer [src]

        1
        -
        y
-y + y*e

$$y e^{\frac{1}{y}} - y$$

=

        1
        -
        y
-y + y*e

$$y e^{\frac{1}{y}} - y$$

-y + y*exp(1/y)

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