Mister Exam

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Integral of d{x}:
Integral of e^2
Integral of 1/sin^3x
Integral of (1/xlnx)
Integral of sqrt(4x-x^2)
Identical expressions
xye^((x^ two)y)
xye to the power of ((x squared )y)
xye to the power of ((x to the power of two)y)
xye((x2)y)
xyex2y
xye^((x²)y)
xye to the power of ((x to the power of 2)y)
xye^x^2y
xye^((x^2)y)dx

Integral of xye^((x^2)y) dx

The solution

You have entered [src]

  1             
  /             
 |              
 |        2     
 |       x *y   
 |  x*y*e     dx
 |              
/               
0

$$\int\limits_{0}^{1} x y e^{x^{2} y}\, dx$$

Integral(x*y*E^(x^2*y), (x, 0, 1))

The answer (Indefinite) [src]

                        //  2             \
  /                     || x              |
 |                      || --    for y = 0|
 |       2              || 2              |
 |      x *y            ||                |
 | x*y*e     dx = C + y*|<  2             |
 |                      || x *y           |
/                       ||e               |
                        ||-----  otherwise|
                        || 2*y            |
                        \\                /

$${{e^{x^2\,y}}\over{2}}$$

Simplify

The answer [src]

       y
  1   e 
- - + --
  2   2

$$y\,\left({{e^{y}}\over{2\,y}}-{{1}\over{2\,y}}\right)$$

       y
  1   e 
- - + --
  2   2

$$\frac{e^{y}}{2} - \frac{1}{2}$$

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

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Identical expressions

Integral of xye^((x^2)y) dx

Limits of integration:

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The solution