Sr Examen
Integral de 1/((x^5+1)^(1/3)) dx
Solución
Ha introducido
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1 / | | 1 | ----------- dx | ________ | 3 / 5 | \/ x + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt[3]{x^{5} + 1}}\, dx$$
Integral(1/((x^5 + 1)^(1/3)), (x, 0, 1))
Respuesta (Indefinida)
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_ / |_ /1/5, 1/3 | 5 pi*I\ | x*Gamma(1/5)* | | | x *e | | 1 2 1 \ 6/5 | / | ----------- dx = C + --------------------------------------- | ________ 5*Gamma(6/5) | 3 / 5 | \/ x + 1 | /
$$\int \frac{1}{\sqrt[3]{x^{5} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{6}{5} \end{matrix}\middle| {x^{5} e^{i \pi}} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
Gráfica
Respuesta
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_
|_ /1/5, 1/3 | \
Gamma(1/5)* | | | -1|
2 1 \ 6/5 | /
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5*Gamma(6/5)
$$\frac{\Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{6}{5} \end{matrix}\middle| {-1} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
=
=
_
|_ /1/5, 1/3 | \
Gamma(1/5)* | | | -1|
2 1 \ 6/5 | /
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5*Gamma(6/5)
$$\frac{\Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{6}{5} \end{matrix}\middle| {-1} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
gamma(1/5)*hyper((1/5, 1/3), (6/5,), -1)/(5*gamma(6/5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.