Sr Examen
Integral de x/(√(Z-2x^4-x^4)) dx
Solución
Ha introducido
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1 / | | x | ------------------ dx | _______________ | / 4 4 | \/ z - 2*x - x | / 0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{- x^{4} + \left(- 2 x^{4} + z\right)}}\, dx$$
Integral(x/sqrt(z - 2*x^4 - x^4), (x, 0, 1))
Respuesta (Indefinida)
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// / ___ 2\ \
|| ___ |\/ 3 *x | |
||-I*\/ 3 *acosh|--------| |
|| | ___ | | 4| |
/ || \ \/ z / |x | |
| ||------------------------- for 3*|--| > 1|
| x || 6 |z | |
| ------------------ dx = C + |< |
| _______________ || / ___ 2\ |
| / 4 4 || ___ |\/ 3 *x | |
| \/ z - 2*x - x || \/ 3 *asin|--------| |
| || | ___ | |
/ || \ \/ z / |
|| -------------------- otherwise |
\\ 6 /
$$\int \frac{x}{\sqrt{- x^{4} + \left(- 2 x^{4} + z\right)}}\, dx = C + \begin{cases} - \frac{\sqrt{3} i \operatorname{acosh}{\left(\frac{\sqrt{3} x^{2}}{\sqrt{z}} \right)}}{6} & \text{for}\: 3 \left|{\frac{x^{4}}{z}}\right| > 1 \\\frac{\sqrt{3} \operatorname{asin}{\left(\frac{\sqrt{3} x^{2}}{\sqrt{z}} \right)}}{6} & \text{otherwise} \end{cases}$$
Respuesta
[src]
1 / | | / 4 | | -I*x 3*x | |---------------------- for ---- > 1 | | ___________ |z| | | / 4 | | ___ / 3*x | |\/ z * / -1 + ---- | | \/ z | < dx | | x | |--------------------- otherwise | | __________ | | / 4 | | ___ / 3*x | |\/ z * / 1 - ---- | | \/ z | \ | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{z} \sqrt{\frac{3 x^{4}}{z} - 1}} & \text{for}\: \frac{3 x^{4}}{\left|{z}\right|} > 1 \\\frac{x}{\sqrt{z} \sqrt{- \frac{3 x^{4}}{z} + 1}} & \text{otherwise} \end{cases}\, dx$$
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1 / | | / 4 | | -I*x 3*x | |---------------------- for ---- > 1 | | ___________ |z| | | / 4 | | ___ / 3*x | |\/ z * / -1 + ---- | | \/ z | < dx | | x | |--------------------- otherwise | | __________ | | / 4 | | ___ / 3*x | |\/ z * / 1 - ---- | | \/ z | \ | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x}{\sqrt{z} \sqrt{\frac{3 x^{4}}{z} - 1}} & \text{for}\: \frac{3 x^{4}}{\left|{z}\right|} > 1 \\\frac{x}{\sqrt{z} \sqrt{- \frac{3 x^{4}}{z} + 1}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-i*x/(sqrt(z)*sqrt(-1 + 3*x^4/z)), 3*x^4/|z| > 1), (x/(sqrt(z)*sqrt(1 - 3*x^4/z)), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.