Sr Examen
Integral de 1/(1+x^4)^(1/3) dx
Solución
Ha introducido
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oo / | | 1 | ----------- dx | ________ | 3 / 4 | \/ 1 + x | / 0
$$\int\limits_{0}^{\infty} \frac{1}{\sqrt[3]{x^{4} + 1}}\, dx$$
Integral(1/((1 + x^4)^(1/3)), (x, 0, oo))
Respuesta (Indefinida)
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_ / |_ /1/4, 1/3 | 4 pi*I\ | x*Gamma(1/4)* | | | x *e | | 1 2 1 \ 5/4 | / | ----------- dx = C + --------------------------------------- | ________ 4*Gamma(5/4) | 3 / 4 | \/ 1 + x | /
$$\int \frac{1}{\sqrt[3]{x^{4} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{3} \\ \frac{5}{4} \end{matrix}\middle| {x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
Respuesta
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Gamma(1/4)*Gamma(1/12)
----------------------
4*Gamma(1/3)
$$\frac{\Gamma\left(\frac{1}{12}\right) \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{1}{3}\right)}$$
=
=
Gamma(1/4)*Gamma(1/12)
----------------------
4*Gamma(1/3)
$$\frac{\Gamma\left(\frac{1}{12}\right) \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{1}{3}\right)}$$
gamma(1/4)*gamma(1/12)/(4*gamma(1/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.