Sr Examen
Integral de x^3/sqrt(1-x^8) dx
Solución
Ha introducido
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1 / | | 3 | x | ----------- dx | ________ | / 8 | \/ 1 - x | / 0
$$\int\limits_{0}^{1} \frac{x^{3}}{\sqrt{1 - x^{8}}}\, dx$$
Integral(x^3/sqrt(1 - x^8), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ // / 4\ \ | ||-I*acosh\x / | 8| | | 3 ||------------- for |x | > 1| | x || 4 | | ----------- dx = C + |< | | ________ || / 4\ | | / 8 || asin\x / | | \/ 1 - x || -------- otherwise | | \\ 4 / /
$$\int \frac{x^{3}}{\sqrt{1 - x^{8}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(x^{4} \right)}}{4} & \text{for}\: \left|{x^{8}}\right| > 1 \\\frac{\operatorname{asin}{\left(x^{4} \right)}}{4} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
1 / | | / 3 | | -I*x 8 | |------------ for x > 1 | | _________ | | / 8 | |\/ -1 + x | < dx | | 3 | | x | |----------- otherwise | | ________ | | / 8 | \\/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x^{3}}{\sqrt{x^{8} - 1}} & \text{for}\: x^{8} > 1 \\\frac{x^{3}}{\sqrt{1 - x^{8}}} & \text{otherwise} \end{cases}\, dx$$
=
=
1 / | | / 3 | | -I*x 8 | |------------ for x > 1 | | _________ | | / 8 | |\/ -1 + x | < dx | | 3 | | x | |----------- otherwise | | ________ | | / 8 | \\/ 1 - x | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x^{3}}{\sqrt{x^{8} - 1}} & \text{for}\: x^{8} > 1 \\\frac{x^{3}}{\sqrt{1 - x^{8}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-i*x^3/sqrt(-1 + x^8), x^8 > 1), (x^3/sqrt(1 - x^8), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.