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Integral of d{x}:
Integral of (1-x^2)^(1/2)
Integral of 1÷(1+x^2)
Integral of 6x^2
Integral of e^(x/2)
Equation:
e^(x/2)
Derivative of:
e^(x/2)
Limit of the function:
e^(x/2)
Identical expressions
e^(x/ two)
e to the power of (x divide by 2)
e to the power of (x divide by two)
e(x/2)
ex/2
e^x/2
e^(x divide by 2)
e^(x/2)dx
Similar expressions
(x^2+2)×e^(x/2)

Solving integrals/ e^(x/2)

Integral of e^(x/2) dx

The solution

You have entered [src]

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

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

Detail solution

Let $u = \frac{x}{2}$ .

Then let $du = \frac{dx}{2}$ and substitute $2 du$ :

$\int 2 e^{u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $2 e^{u}$
Now substitute $u$ back in:

$2 e^{\frac{x}{2}}$
Now simplify:

$2 e^{\frac{x}{2}}$
Add the constant of integration:

$2 e^{\frac{x}{2}}+ \mathrm{constant}$

The answer is:

2 e^{\frac{x}{2}}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                
 |                 
 |  x             x
 |  -             -
 |  2             2
 | E  dx = C + 2*e 
 |                 
/

\int e^{\frac{x}{2}}\, dx = C + 2 e^{\frac{x}{2}}

Simplify

The graph

Plot the graph f(x)

The answer [src]

        1/2
-2 + 2*e

-2 + 2 e^{\frac{1}{2}}

=

        1/2
-2 + 2*e

-2 + 2 e^{\frac{1}{2}}

-2 + 2*exp(1/2)

Numerical answer [src]

1.29744254140026

1.29744254140026

The graph

Integral of e^(x/2) dx

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