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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^4lnx
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Integral of dx/(1-4*x^2)
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Integral of (4x-x^2)dx
- Integral of log(x+1)/(x^2+1)
- The double integral of:
- ye^(xy/2)
- ye^(xy/2)
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Identical expressions
- ye^(xy/ two)
- ye to the power of (xy divide by 2)
- ye to the power of (xy divide by two)
- ye(xy/2)
- yexy/2
- ye^xy/2
- ye^(xy divide by 2)
- ye^(xy/2)dx
Integral of ye^(xy/2) dy
The solution
You have entered
[src]
1 / | | x*y | --- | 2 | y*E dy | / 0
$$\int\limits_{0}^{1} e^{\frac{x y}{2}} y\, dy$$
Integral(y*E^((x*y)/2), (y, 0, 1))
The answer (Indefinite)
[src]
// x*y \
/ || --- |
| || 2 |
| x*y ||(-4 + 2*x*y)*e 2 |
| --- ||----------------- for x != 0|
| 2 || 2 |
| y*E dy = C + |< x |
| || |
/ || 2 |
|| y |
|| -- otherwise |
|| 2 |
\\ /
$$\int e^{\frac{x y}{2}} y\, dy = C + \begin{cases} \frac{\left(2 x y - 4\right) e^{\frac{x y}{2}}}{x^{2}} & \text{for}\: x^{2} \neq 0 \\\frac{y^{2}}{2} & \text{otherwise} \end{cases}$$
The answer
[src]
/ x | - | 2 |4 (-4 + 2*x)*e <-- + ------------- for And(x > -oo, x < oo, x != 0) | 2 2 |x x | \ 1/2 otherwise
$$\begin{cases} \frac{\left(2 x - 4\right) e^{\frac{x}{2}}}{x^{2}} + \frac{4}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
=
=
/ x | - | 2 |4 (-4 + 2*x)*e <-- + ------------- for And(x > -oo, x < oo, x != 0) | 2 2 |x x | \ 1/2 otherwise
$$\begin{cases} \frac{\left(2 x - 4\right) e^{\frac{x}{2}}}{x^{2}} + \frac{4}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
Piecewise((4/x^2 + (-4 + 2*x)*exp(x/2)/x^2, (x > -oo)∧(x < oo)∧(Ne(x, 0))), (1/2, True))
Use the examples entering the upper and lower limits of integration.