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Integral of 1/(1+4x^2)
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Integral of x*3^x
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Identical expressions
- ye^(yx/ two)
- ye to the power of (yx divide by 2)
- ye to the power of (yx divide by two)
- ye(yx/2)
- yeyx/2
- ye^yx/2
- ye^(yx divide by 2)
- ye^(yx/2)dx
Integral of ye^(yx/2) dy
The solution
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[src]
1 / | | y*x | --- | 2 | y*E dy | / 0
$$\int\limits_{0}^{1} e^{\frac{x y}{2}} y\, dy$$
Integral(y*E^((y*x)/2), (y, 0, 1))
The answer (Indefinite)
[src]
// y*x \
/ || --- |
| || 2 |
| y*x ||(-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.