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Identical expressions
- x*y*e^(x*y)*dx
- x multiply by y multiply by e to the power of (x multiply by y) multiply by dx
- x*y*e(x*y)*dx
- x*y*ex*y*dx
- xye^(xy)dx
- xye(xy)dx
- xyexydx
- xye^xydx
Integral of x*y*e^(x*y)*dx dx
The solution
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[src]
1 / | | x*y | x*y*e *1 dx | / 0
$$\int\limits_{0}^{1} x y e^{x y} 1\, dx$$
Integral(x*y*E^(x*y)*1, (x, 0, 1))
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*|
$$\int x y e^{x y} 1\, dx = C + y \left(x \left(\begin{cases} x & \text{for}\: y = 0 \\\frac{e^{x y}}{y} & \text{otherwise} \end{cases}\right) - \begin{cases} \frac{x^{2}}{2} & \text{for}\: y = 0 \\\begin{cases} \frac{e^{x y}}{y^{2}} & \text{for}\: y^{2} \neq 0 \\\frac{x}{y} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
The answer
[src]
/ 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.