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