Integral of x*y*e^(x*y)*dx dx
The solution
The answer (Indefinite)
[src]
/ // 2 \ \
| || x | |
| || -- for y = 0| |
| || 2 | |
/ | || | // x for y = 0\|
| | ||/ x*y | || ||
| x*y | |||e 2 | || x*y ||
| x*y*e *1 dx = C + y*|- |<|---- for y != 0 | + x*|
$$\int x y e^{x y} 1\, dx = C + y \left(x \left(\begin{cases} x & \text{for}\: y = 0 \\\frac{e^{x y}}{y} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: y = 0 \\\begin{cases} \frac{e^{x y}}{y^{2}} & \text{for}\: y^{2} \neq 0 \\\frac{x}{y} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
/ y
|1 (-1 + y)*e
|- + ----------- for And(y > -oo, y < oo, y != 0)
|y y
<
| y
| - otherwise
| 2
\
$$\begin{cases} \frac{\left(y - 1\right) e^{y}}{y} + \frac{1}{y} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\\frac{y}{2} & \text{otherwise} \end{cases}$$
=
/ y
|1 (-1 + y)*e
|- + ----------- for And(y > -oo, y < oo, y != 0)
|y y
<
| y
| - otherwise
| 2
\
$$\begin{cases} \frac{\left(y - 1\right) e^{y}}{y} + \frac{1}{y} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\\frac{y}{2} & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.