Sr Examen
Integral de x/(2-x^4)^1/2 dx
Solución
Ha introducido
[src]
1 / | | x | ----------- dx | ________ | / 4 | \/ 2 - x | / 0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{2 - x^{4}}}\, dx$$
Integral(x/sqrt(2 - x^4), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ 2\ \
|| |\/ 2 *x | |
||-I*acosh|--------| | 4| |
/ || \ 2 / |x | |
| ||------------------- for ---- > 1|
| x || 2 2 |
| ----------- dx = C + |< |
| ________ || / ___ 2\ |
| / 4 || |\/ 2 *x | |
| \/ 2 - x || asin|--------| |
| || \ 2 / |
/ || -------------- otherwise |
\\ 2 /
$$\int \frac{x}{\sqrt{2 - x^{4}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{\sqrt{2} x^{2}}{2} \right)}}{2} & \text{for}\: \frac{\left|{x^{4}}\right|}{2} > 1 \\\frac{\operatorname{asin}{\left(\frac{\sqrt{2} x^{2}}{2} \right)}}{2} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
1 / | | / ___ 4 | | -I*x*\/ 2 x | |---------------- for -- > 1 | | _________ 2 | | / 4 | | / x | |2* / -1 + -- | | \/ 2 | < dx | | ___ | | x*\/ 2 | |--------------- otherwise | | ________ | | / 4 | | / x | |2* / 1 - -- | \ \/ 2 | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{\sqrt{2} i x}{2 \sqrt{\frac{x^{4}}{2} - 1}} & \text{for}\: \frac{x^{4}}{2} > 1 \\\frac{\sqrt{2} x}{2 \sqrt{1 - \frac{x^{4}}{2}}} & \text{otherwise} \end{cases}\, dx$$
=
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1 / | | / ___ 4 | | -I*x*\/ 2 x | |---------------- for -- > 1 | | _________ 2 | | / 4 | | / x | |2* / -1 + -- | | \/ 2 | < dx | | ___ | | x*\/ 2 | |--------------- otherwise | | ________ | | / 4 | | / x | |2* / 1 - -- | \ \/ 2 | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{\sqrt{2} i x}{2 \sqrt{\frac{x^{4}}{2} - 1}} & \text{for}\: \frac{x^{4}}{2} > 1 \\\frac{\sqrt{2} x}{2 \sqrt{1 - \frac{x^{4}}{2}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-i*x*sqrt(2)/(2*sqrt(-1 + x^4/2)), x^4/2 > 1), (x*sqrt(2)/(2*sqrt(1 - x^4/2)), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.