Sr Examen
Integral de 1/(sqrt((2-5x)^7)^1/3) dx
Solución
Ha introducido
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1 / | | 1 | --------------------- dx | _________________ | / ____________ | 3 / / 7 | \/ \/ (2 - 5*x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt[3]{\sqrt{\left(2 - 5 x\right)^{7}}}}\, dx$$
Integral(1/((sqrt((2 - 5*x)^7))^(1/3)), (x, 0, 1))
Respuesta
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5/6 2/3 5/6
2/3 / 5/6\ (-3) *Gamma(-1/6) (-1) *2 *Gamma(-1/6)
oo*(-1) - oo*sign\(-5) / - ------------------- + ------------------------
15*Gamma(5/6) 10*Gamma(5/6)
$$- \infty \operatorname{sign}{\left(\left(-5\right)^{\frac{5}{6}} \right)} + \frac{\left(-1\right)^{\frac{2}{3}} \cdot 2^{\frac{5}{6}} \Gamma\left(- \frac{1}{6}\right)}{10 \Gamma\left(\frac{5}{6}\right)} - \frac{\left(-3\right)^{\frac{5}{6}} \Gamma\left(- \frac{1}{6}\right)}{15 \Gamma\left(\frac{5}{6}\right)} + \infty \left(-1\right)^{\frac{2}{3}}$$
=
=
5/6 2/3 5/6
2/3 / 5/6\ (-3) *Gamma(-1/6) (-1) *2 *Gamma(-1/6)
oo*(-1) - oo*sign\(-5) / - ------------------- + ------------------------
15*Gamma(5/6) 10*Gamma(5/6)
$$- \infty \operatorname{sign}{\left(\left(-5\right)^{\frac{5}{6}} \right)} + \frac{\left(-1\right)^{\frac{2}{3}} \cdot 2^{\frac{5}{6}} \Gamma\left(- \frac{1}{6}\right)}{10 \Gamma\left(\frac{5}{6}\right)} - \frac{\left(-3\right)^{\frac{5}{6}} \Gamma\left(- \frac{1}{6}\right)}{15 \Gamma\left(\frac{5}{6}\right)} + \infty \left(-1\right)^{\frac{2}{3}}$$
oo*(-1)^(2/3) - oo*sign((-5)^(5/6)) - (-3)^(5/6)*gamma(-1/6)/(15*gamma(5/6)) + (-1)^(2/3)*2^(5/6)*gamma(-1/6)/(10*gamma(5/6))
Respuesta numérica
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(3.5598700394849 - 1.35671508576365j)
(3.5598700394849 - 1.35671508576365j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.