Sr Examen
Integral de 5*x/sqrt(16-x^4) dx
Solución
Ha introducido
[src]
2 / | | 5*x | ------------ dx | _________ | / 4 | \/ 16 - x | / 0
$$\int\limits_{0}^{2} \frac{5 x}{\sqrt{16 - x^{4}}}\, dx$$
Integral((5*x)/sqrt(16 - x^4), (x, 0, 2))
Respuesta (Indefinida)
[src]
// / 2\ \
|| |x | |
||-5*I*acosh|--| | 4| |
/ || \4 / |x | |
| ||-------------- for ---- > 1|
| 5*x || 2 16 |
| ------------ dx = C + |< |
| _________ || / 2\ |
| / 4 || |x | |
| \/ 16 - x || 5*asin|--| |
| || \4 / |
/ || ---------- otherwise |
\\ 2 /
$$\int \frac{5 x}{\sqrt{16 - x^{4}}}\, dx = C + \begin{cases} - \frac{5 i \operatorname{acosh}{\left(\frac{x^{2}}{4} \right)}}{2} & \text{for}\: \frac{\left|{x^{4}}\right|}{16} > 1 \\\frac{5 \operatorname{asin}{\left(\frac{x^{2}}{4} \right)}}{2} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
2 / | | / 4 | | -5*I*x x | |---------------- for -- > 1 | | _________ 16 | | / 4 | | / x | |4* / -1 + -- | | \/ 16 | < dx | | 5*x | |--------------- otherwise | | ________ | | / 4 | | / x | |4* / 1 - -- | | \/ 16 | \ | / 0
$$\int\limits_{0}^{2} \begin{cases} - \frac{5 i x}{4 \sqrt{\frac{x^{4}}{16} - 1}} & \text{for}\: \frac{x^{4}}{16} > 1 \\\frac{5 x}{4 \sqrt{1 - \frac{x^{4}}{16}}} & \text{otherwise} \end{cases}\, dx$$
=
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2 / | | / 4 | | -5*I*x x | |---------------- for -- > 1 | | _________ 16 | | / 4 | | / x | |4* / -1 + -- | | \/ 16 | < dx | | 5*x | |--------------- otherwise | | ________ | | / 4 | | / x | |4* / 1 - -- | | \/ 16 | \ | / 0
$$\int\limits_{0}^{2} \begin{cases} - \frac{5 i x}{4 \sqrt{\frac{x^{4}}{16} - 1}} & \text{for}\: \frac{x^{4}}{16} > 1 \\\frac{5 x}{4 \sqrt{1 - \frac{x^{4}}{16}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-5*i*x/(4*sqrt(-1 + x^4/16)), x^4/16 > 1), (5*x/(4*sqrt(1 - x^4/16)), True)), (x, 0, 2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.