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