Sr Examen
Integral de x^4*dx/sqrt(x^10-3) dx
Solución
Ha introducido
[src]
1 / | | 4 | x | ------------ dx | _________ | / 10 | \/ x - 3 | / 0
$$\int\limits_{0}^{1} \frac{x^{4}}{\sqrt{x^{10} - 3}}\, dx$$
Integral(x^4/sqrt(x^10 - 3), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ 5\ \
|| |\/ 3 *x | |
/ || acosh|--------| | 10| |
| || \ 3 / |x | |
| 4 || --------------- for ----- > 1|
| x || 5 3 |
| ------------ dx = C + |< |
| _________ || / ___ 5\ |
| / 10 || |\/ 3 *x | |
| \/ x - 3 ||-I*asin|--------| |
| || \ 3 / |
/ ||------------------ otherwise |
\\ 5 /
$$\int \frac{x^{4}}{\sqrt{x^{10} - 3}}\, dx = C + \begin{cases} \frac{\operatorname{acosh}{\left(\frac{\sqrt{3} x^{5}}{3} \right)}}{5} & \text{for}\: \frac{\left|{x^{10}}\right|}{3} > 1 \\- \frac{i \operatorname{asin}{\left(\frac{\sqrt{3} x^{5}}{3} \right)}}{5} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
1 / | | / ___ 4 10 | | \/ 3 *x x | |----------------- for --- > 1 | | __________ 3 | | / 10 | | / x | |3* / -1 + --- | | \/ 3 | < dx | | ___ 4 | | -I*\/ 3 *x | |---------------- otherwise | | _________ | | / 10 | | / x | |3* / 1 - --- | \ \/ 3 | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{\sqrt{3} x^{4}}{3 \sqrt{\frac{x^{10}}{3} - 1}} & \text{for}\: \frac{x^{10}}{3} > 1 \\- \frac{\sqrt{3} i x^{4}}{3 \sqrt{1 - \frac{x^{10}}{3}}} & \text{otherwise} \end{cases}\, dx$$
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1 / | | / ___ 4 10 | | \/ 3 *x x | |----------------- for --- > 1 | | __________ 3 | | / 10 | | / x | |3* / -1 + --- | | \/ 3 | < dx | | ___ 4 | | -I*\/ 3 *x | |---------------- otherwise | | _________ | | / 10 | | / x | |3* / 1 - --- | \ \/ 3 | / 0
$$\int\limits_{0}^{1} \begin{cases} \frac{\sqrt{3} x^{4}}{3 \sqrt{\frac{x^{10}}{3} - 1}} & \text{for}\: \frac{x^{10}}{3} > 1 \\- \frac{\sqrt{3} i x^{4}}{3 \sqrt{1 - \frac{x^{10}}{3}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((sqrt(3)*x^4/(3*sqrt(-1 + x^10/3)), x^10/3 > 1), (-i*sqrt(3)*x^4/(3*sqrt(1 - x^10/3)), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.