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e^(x/2)

Integral of e^(x/2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
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01ex2dx\int\limits_{0}^{1} e^{\frac{x}{2}}\, dx
Integral(E^(x/2), (x, 0, 1))
Detail solution
  1. Let u=x2u = \frac{x}{2}.

    Then let du=dx2du = \frac{dx}{2} and substitute 2du2 du:

    2eudu\int 2 e^{u}\, du

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

      False\text{False}

      1. The integral of the exponential function is itself.

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

      So, the result is: 2eu2 e^{u}

    Now substitute uu back in:

    2ex22 e^{\frac{x}{2}}

  2. Now simplify:

    2ex22 e^{\frac{x}{2}}

  3. Add the constant of integration:

    2ex2+constant2 e^{\frac{x}{2}}+ \mathrm{constant}


The answer is:

2ex2+constant2 e^{\frac{x}{2}}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                
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ex2dx=C+2ex2\int e^{\frac{x}{2}}\, dx = C + 2 e^{\frac{x}{2}}
The graph
0.001.000.100.200.300.400.500.600.700.800.900.05.0
The answer [src]
        1/2
-2 + 2*e   
2+2e12-2 + 2 e^{\frac{1}{2}}
=
=
        1/2
-2 + 2*e   
2+2e12-2 + 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.