Mister Exam

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Integral of d{x}:
Integral of xye^(xy^2)dy
Integral of 2/x³
Integral of sin^4(x)*cos^6(x)
Integral of sqrt(6x-x^2)
Identical expressions
xye^(xy^ two)dy
xye to the power of (xy squared )dy
xye to the power of (xy to the power of two)dy
xye(xy2)dy
xyexy2dy
xye^(xy²)dy
xye to the power of (xy to the power of 2)dy
xye^xy^2dy
xye^(xy^2)dydx

Integral of xye^(xy^2)dy dx

The solution

You have entered [src]

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

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

Simplify

The answer (Indefinite) [src]

                          //  2             \
  /                       || y              |
 |                        || --    for x = 0|
 |         2              || 2              |
 |      x*y               ||                |
 | x*y*e    *1 dy = C + x*|<    2           |
 |                        || x*y            |
/                         ||e               |
                          ||-----  otherwise|
                          || 2*x            |
                          \\                /

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

Simplify

The answer [src]

       x
  1   e 
- - + --
  2   2

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

       x
  1   e 
- - + --
  2   2

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

Simplify

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

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Identical expressions

Integral of xye^(xy^2)dy dx

Limits of integration:

The graph:

Piecewise:

The solution