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