Integral de x^(-3)*(1+x^(-1))^(-1/5) dx
Solución
Respuesta (Indefinida)
[src]
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| 9/5 14/5 4/5 4/5 2 4/5
| 1 4*x *Gamma(-9/5)*Gamma(14/5) 4*x *Gamma(-9/5)*Gamma(14/5) 4*(1 + x) *Gamma(1/5)*Gamma(9/5) x*(1 + x) *Gamma(1/5)*Gamma(9/5) 5*x *(1 + x) *Gamma(1/5)*Gamma(9/5)
| -------------- dx = C - -------------------------------------------------------------- - -------------------------------------------------------------- - -------------------------------------------------------------- + -------------------------------------------------------------- + --------------------------------------------------------------
| _______ 9/5 14/5 9/5 14/5 9/5 14/5 9/5 14/5 9/5 14/5
| 3 / 1 4*x *Gamma(1/5)*Gamma(14/5) + 4*x *Gamma(1/5)*Gamma(14/5) 4*x *Gamma(1/5)*Gamma(14/5) + 4*x *Gamma(1/5)*Gamma(14/5) 4*x *Gamma(1/5)*Gamma(14/5) + 4*x *Gamma(1/5)*Gamma(14/5) 4*x *Gamma(1/5)*Gamma(14/5) + 4*x *Gamma(1/5)*Gamma(14/5) 4*x *Gamma(1/5)*Gamma(14/5) + 4*x *Gamma(1/5)*Gamma(14/5)
| x *5 / 1 + -
| \/ x
|
/
$$\int \frac{1}{x^{3} \sqrt[5]{1 + \frac{1}{x}}}\, dx = C - \frac{4 x^{\frac{14}{5}} \Gamma\left(- \frac{9}{5}\right) \Gamma\left(\frac{14}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)} - \frac{4 x^{\frac{9}{5}} \Gamma\left(- \frac{9}{5}\right) \Gamma\left(\frac{14}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)} + \frac{5 x^{2} \left(x + 1\right)^{\frac{4}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{9}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)} + \frac{x \left(x + 1\right)^{\frac{4}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{9}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)} - \frac{4 \left(x + 1\right)^{\frac{4}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{9}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.