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pi(sqrt(x)e^x)^2
Solving integrals/ pi(sqrt(x)e^x)^2

Integral of pi(sqrt(x)e^x)^2 dx

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The solution

You have entered [src] 
  1                  
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 |  pi*\\/ x *e /  dx
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∫01π(xex)2 dx\int\limits_{0}^{1} \pi \left(\sqrt{x} e^{x}\right)^{2}\, dx 
Integral(pi*(sqrt(x)*E^x)^2, (x, 0, 1))
Detail solution

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

    ∫π(xex)2 dx=π∫(xex)2 dx\int \pi \left(\sqrt{x} e^{x}\right)^{2}\, dx = \pi \int \left(\sqrt{x} e^{x}\right)^{2}\, dx

    1. Don't know the steps in finding this integral.

      But the integral is

      (2x−1)e2x4\frac{\left(2 x - 1\right) e^{2 x}}{4}

    So, the result is: π(2x−1)e2x4\frac{\pi \left(2 x - 1\right) e^{2 x}}{4}

  2. Add the constant of integration:

    π(2x−1)e2x4+constant\frac{\pi \left(2 x - 1\right) e^{2 x}}{4}+ \mathrm{constant}

The answer is:

π(2x−1)e2x4+constant\frac{\pi \left(2 x - 1\right) e^{2 x}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 |    /  ___  x\           pi*(-1 + 2*x)*e   
 | pi*\\/ x *e /  dx = C + ------------------
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π (2 x−1) e2 x4{{\pi\,\left(2\,x-1\right)\,e^{2\,x}}\over{4}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-2525
Plot the graph f(x)
The answer [src] 
         2
pi   pi*e 
-- + -----
4      4
(e24+14) π\left({{e^2}\over{4}}+{{1}\over{4}}\right)\,\pi 
=
= 
         2
pi   pi*e 
-- + -----
4      4
π4+πe24\frac{\pi}{4} + \frac{\pi e^{2}}{4}
Упростить
Numerical answer [src] 
6.5887492527383
6.5887492527383
The graph
Integral of pi(sqrt(x)e^x)^2 dx

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

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