Sr Examen
Integral de cbrt(x)/(5-x)^(1/4) dx
Solución
Ha introducido
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4 / | | 3 ___ | \/ x | --------- dx | 4 _______ | \/ 5 - x | / 0
$$\int\limits_{0}^{4} \frac{\sqrt[3]{x}}{\sqrt[4]{5 - x}}\, dx$$
Integral(x^(1/3)/(5 - x)^(1/4), (x, 0, 4))
Respuesta (Indefinida)
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/ _ / | 2*pi*I\ | 3/4 4/3 |_ |1/4, 4/3 | x*e | | 3 ___ 5 *x *Gamma(4/3)* | | | ---------| | \/ x 2 1 \ 7/3 | 5 / | --------- dx = C + ------------------------------------------------ | 4 _______ 5*Gamma(7/3) | \/ 5 - x | /
$$\int \frac{\sqrt[3]{x}}{\sqrt[4]{5 - x}}\, dx = C + \frac{5^{\frac{3}{4}} x^{\frac{4}{3}} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{x e^{2 i \pi}}{5}} \right)}}{5 \Gamma\left(\frac{7}{3}\right)}$$
Gráfica
Respuesta
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2/3 3/4 |_ /1/4, 4/3 | \
4*2 *5 *Gamma(4/3)* | | | 4/5|
2 1 \ 7/3 | /
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5*Gamma(7/3)
$$\frac{4 \cdot 2^{\frac{2}{3}} \cdot 5^{\frac{3}{4}} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{4}{5}} \right)}}{5 \Gamma\left(\frac{7}{3}\right)}$$
=
=
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2/3 3/4 |_ /1/4, 4/3 | \
4*2 *5 *Gamma(4/3)* | | | 4/5|
2 1 \ 7/3 | /
--------------------------------------------
5*Gamma(7/3)
$$\frac{4 \cdot 2^{\frac{2}{3}} \cdot 5^{\frac{3}{4}} \Gamma\left(\frac{4}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{4}{3} \\ \frac{7}{3} \end{matrix}\middle| {\frac{4}{5}} \right)}}{5 \Gamma\left(\frac{7}{3}\right)}$$
4*2^(2/3)*5^(3/4)*gamma(4/3)*hyper((1/4, 4/3), (7/3,), 4/5)/(5*gamma(7/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.