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e^5*x*dx
Solving integrals/ e^5*x*dx

Integral of e^5*x*dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |   5     
 |  E *x dx
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0
∫01e5x dx\int\limits_{0}^{1} e^{5} x\, dx 
Integral(E^5*x, (x, 0, 1))
Detail solution

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

    ∫e5x dx=e5∫x dx\int e^{5} x\, dx = e^{5} \int x\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    So, the result is: x2e52\frac{x^{2} e^{5}}{2}

  2. Add the constant of integration:

    x2e52+constant\frac{x^{2} e^{5}}{2}+ \mathrm{constant}

The answer is:

x2e52+constant\frac{x^{2} e^{5}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 |                2  5
 |  5            x *e 
 | E *x dx = C + -----
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∫e5x dx=C+x2e52\int e^{5} x\, dx = C + \frac{x^{2} e^{5}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900200
Plot the graph f(x)
The answer [src] 
 5
e 
--
2
e52\frac{e^{5}}{2} 
=
= 
 5
e 
--
2
e52\frac{e^{5}}{2} 
exp(5)/2
Numerical answer [src] 
74.2065795512883
74.2065795512883
The graph
Integral of e^5*x*dx dx

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

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