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

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

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

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |               2   
 |     /  ___  x\    
 |  pi*\\/ x *e /  dx
 |                   
/                    
0

$$\int\limits_{0}^{1} \pi \left(\sqrt{x} e^{x}\right)^{2}\, dx$$

Integral(pi*(sqrt(x)*E^x)^2, (x, 0, 1))

Detail solution

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

$\int \pi \left(\sqrt{x} e^{x}\right)^{2}\, dx = \pi \int \left(\sqrt{x} e^{x}\right)^{2}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{\left(2 x - 1\right) e^{2 x}}{4}$
So, the result is: $\frac{\pi \left(2 x - 1\right) e^{2 x}}{4}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                          
 |                                           
 |              2                         2*x
 |    /  ___  x\           pi*(-1 + 2*x)*e   
 | pi*\\/ x *e /  dx = C + ------------------
 |                                 4         
/

$${{\pi\,\left(2\,x-1\right)\,e^{2\,x}}\over{4}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         2
pi   pi*e 
-- + -----
4      4

$$\left({{e^2}\over{4}}+{{1}\over{4}}\right)\,\pi$$

         2
pi   pi*e 
-- + -----
4      4

$$\frac{\pi}{4} + \frac{\pi e^{2}}{4}$$

Упростить

Numerical answer [src]

6.5887492527383

6.5887492527383

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution