Sr Examen
Integral de 4*x^3*dx/sqrt(4-x^8) dx
Solución
Ha introducido
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1 / | | 3 | 4*x | ----------- dx | ________ | / 8 | \/ 4 - x | / 0
$$\int\limits_{0}^{1} \frac{4 x^{3}}{\sqrt{4 - x^{8}}}\, dx$$
Integral((4*x^3)/sqrt(4 - x^8), (x, 0, 1))
Respuesta (Indefinida)
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/ // / 4\ | 8| \ | || |x | |x | | | 3 ||-I*acosh|--| for ---- > 1| | 4*x || \2 / 4 | | ----------- dx = C + |< | | ________ || / 4\ | | / 8 || |x | | | \/ 4 - x || asin|--| otherwise | | \\ \2 / / /
$$\int \frac{4 x^{3}}{\sqrt{4 - x^{8}}}\, dx = C + \begin{cases} - i \operatorname{acosh}{\left(\frac{x^{4}}{2} \right)} & \text{for}\: \frac{\left|{x^{8}}\right|}{4} > 1 \\\operatorname{asin}{\left(\frac{x^{4}}{2} \right)} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
1 / | | / 3 8 | | -2*I*x x | |-------------- for -- > 1 | | _________ 4 | | / 8 | | / x | | / -1 + -- | |\/ 4 | < dx | | 3 | | 2*x | |------------- otherwise | | ________ | | / 8 | | / x | | / 1 - -- | \\/ 4 | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{2 i x^{3}}{\sqrt{\frac{x^{8}}{4} - 1}} & \text{for}\: \frac{x^{8}}{4} > 1 \\\frac{2 x^{3}}{\sqrt{1 - \frac{x^{8}}{4}}} & \text{otherwise} \end{cases}\, dx$$
=
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1 / | | / 3 8 | | -2*I*x x | |-------------- for -- > 1 | | _________ 4 | | / 8 | | / x | | / -1 + -- | |\/ 4 | < dx | | 3 | | 2*x | |------------- otherwise | | ________ | | / 8 | | / x | | / 1 - -- | \\/ 4 | / 0
$$\int\limits_{0}^{1} \begin{cases} - \frac{2 i x^{3}}{\sqrt{\frac{x^{8}}{4} - 1}} & \text{for}\: \frac{x^{8}}{4} > 1 \\\frac{2 x^{3}}{\sqrt{1 - \frac{x^{8}}{4}}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((-2*i*x^3/sqrt(-1 + x^8/4), x^8/4 > 1), (2*x^3/sqrt(1 - x^8/4), True)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.