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x^2*e^2*x
Solving integrals/ x^2*e^2*x

Integral of x^2*e^2*x 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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 |  x *E *x dx
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∫01xe2x2 dx\int\limits_{0}^{1} x e^{2} x^{2}\, dx 
Integral((x^2*E^2)*x, (x, 0, 1))
Detail solution

  1. Let u=x2u = x^{2}.

    Then let du=2xdxdu = 2 x dx and substitute due22\frac{du e^{2}}{2}:

    ∫ue22 du\int \frac{u e^{2}}{2}\, du

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

      ∫u du=e2∫u du2\int u\, du = \frac{e^{2} \int u\, du}{2}

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫u du=u22\int u\, du = \frac{u^{2}}{2}

      So, the result is: u2e24\frac{u^{2} e^{2}}{4}

    Now substitute uu back in:

    x4e24\frac{x^{4} e^{2}}{4}

  2. Add the constant of integration:

    x4e24+constant\frac{x^{4} e^{2}}{4}+ \mathrm{constant}

The answer is:

x4e24+constant\frac{x^{4} e^{2}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 |  2  2            x *e 
 | x *E *x dx = C + -----
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∫xe2x2 dx=C+x4e24\int x e^{2} x^{2}\, dx = C + \frac{x^{4} e^{2}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
 2
e 
--
4
e24\frac{e^{2}}{4} 
=
= 
 2
e 
--
4
e24\frac{e^{2}}{4} 
exp(2)/4
Numerical answer [src] 
1.84726402473266
1.84726402473266
The graph
Integral of x^2*e^2*x dx

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

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