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