Sr Examen
Integral de x^(-3)*(1+x^(-1))^(-1/5) dx
Solución
Ha introducido
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1 / | | 1 | -------------- dx | _______ | 3 / 1 | x *5 / 1 + - | \/ x | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{3} \sqrt[5]{1 + \frac{1}{x}}}\, dx$$
Integral(1/(x^3*(1 + 1/x)^(1/5)), (x, 0, 1))
Respuesta (Indefinida)
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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.