Sr Examen
Integral de x/sqrt(x^5+1) dx
Solución
Ha introducido
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1 / | | x | ----------- dx | ________ | / 5 | \/ x + 1 | / 0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{x^{5} + 1}}\, dx$$
Integral(x/sqrt(x^5 + 1), (x, 0, 1))
Respuesta (Indefinida)
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_ / 2 |_ /2/5, 1/2 | 5 pi*I\ | x *Gamma(2/5)* | | | x *e | | x 2 1 \ 7/5 | / | ----------- dx = C + ---------------------------------------- | ________ 5*Gamma(7/5) | / 5 | \/ x + 1 | /
$$\int \frac{x}{\sqrt{x^{5} + 1}}\, dx = C + \frac{x^{2} \Gamma\left(\frac{2}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{5}, \frac{1}{2} \\ \frac{7}{5} \end{matrix}\middle| {x^{5} e^{i \pi}} \right)}}{5 \Gamma\left(\frac{7}{5}\right)}$$
Gráfica
Respuesta
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_
|_ /2/5, 1/2 | \
Gamma(2/5)* | | | -1|
2 1 \ 7/5 | /
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5*Gamma(7/5)
$$\frac{\Gamma\left(\frac{2}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{5}, \frac{1}{2} \\ \frac{7}{5} \end{matrix}\middle| {-1} \right)}}{5 \Gamma\left(\frac{7}{5}\right)}$$
=
=
_
|_ /2/5, 1/2 | \
Gamma(2/5)* | | | -1|
2 1 \ 7/5 | /
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5*Gamma(7/5)
$$\frac{\Gamma\left(\frac{2}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{5}, \frac{1}{2} \\ \frac{7}{5} \end{matrix}\middle| {-1} \right)}}{5 \Gamma\left(\frac{7}{5}\right)}$$
gamma(2/5)*hyper((2/5, 1/2), (7/5,), -1)/(5*gamma(7/5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.