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Integral of d{x}:
Integral of e^(-x)
Integral of -sin(x)
Integral of cos(x/2)
Integral of x-2
Identical expressions
two ^(x/y)
2 to the power of (x divide by y)
two to the power of (x divide by y)
2(x/y)
2x/y
2^x/y
2^(x divide by y)
2^(x/y)dx

Integral of 2^(x/y) dx

The solution

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$$\int\limits_{0}^{1} 2^{\frac{x}{y}}\, dx$$

Integral(2^(x/y), (x, 0, 1))

Detail solution

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

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

$\int 2^{u} y\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2^{u}\, du = y \int 2^{u}\, du$
  1. The integral of an exponential function is itself divided by the natural logarithm of the base.
    
    $\int 2^{u}\, du = \frac{2^{u}}{\log{\left(2 \right)}}$
  So, the result is: $\frac{2^{u} y}{\log{\left(2 \right)}}$
Now substitute $u$ back in:

$\frac{2^{\frac{x}{y}} y}{\log{\left(2 \right)}}$
Add the constant of integration:

$\frac{2^{\frac{x}{y}} y}{\log{\left(2 \right)}}+ \mathrm{constant}$

The answer is:

$\frac{2^{\frac{x}{y}} y}{\log{\left(2 \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |                 x 
 |  x              - 
 |  -              y 
 |  y           y*2  
 | 2  dx = C + ------
 |             log(2)
/

$$\int 2^{\frac{x}{y}}\, dx = \frac{2^{\frac{x}{y}} y}{\log{\left(2 \right)}} + C$$

Simplify

The answer [src]

             y ___
    y      y*\/ 2 
- ------ + -------
  log(2)    log(2)

$$\frac{2^{\frac{1}{y}} y}{\log{\left(2 \right)}} - \frac{y}{\log{\left(2 \right)}}$$

             y ___
    y      y*\/ 2 
- ------ + -------
  log(2)    log(2)

$$\frac{2^{\frac{1}{y}} y}{\log{\left(2 \right)}} - \frac{y}{\log{\left(2 \right)}}$$

-y/log(2) + y*2^(1/y)/log(2)

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

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Identical expressions

Integral of 2^(x/y) dx

Limits of integration:

The graph:

Piecewise:

The solution