Sr Examen
Integral de root(9x^5-8) dx
Solución
Ha introducido
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1 / | | __________ | / 5 | \/ 9*x - 8 dx | / 0
$$\int\limits_{0}^{1} \sqrt{9 x^{5} - 8}\, dx$$
Integral(sqrt(9*x^5 - 8), (x, 0, 1))
Respuesta (Indefinida)
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/ _ / | 5\ | ___ |_ |-1/2, 1/5 | 9*x | | __________ 2*I*x*\/ 2 *Gamma(1/5)* | | | ----| | / 5 2 1 \ 6/5 | 8 / | \/ 9*x - 8 dx = C + ---------------------------------------------- | 5*Gamma(6/5) /
$$\int \sqrt{9 x^{5} - 8}\, dx = C + \frac{2 \sqrt{2} i x \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{5} \\ \frac{6}{5} \end{matrix}\middle| {\frac{9 x^{5}}{8}} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
Gráfica
Respuesta
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_
___ |_ /-1/2, 1/5 | \
2*I*\/ 2 *Gamma(1/5)* | | | 9/8|
2 1 \ 6/5 | /
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5*Gamma(6/5)
$$\frac{2 \sqrt{2} i \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{5} \\ \frac{6}{5} \end{matrix}\middle| {\frac{9}{8}} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
=
=
_
___ |_ /-1/2, 1/5 | \
2*I*\/ 2 *Gamma(1/5)* | | | 9/8|
2 1 \ 6/5 | /
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5*Gamma(6/5)
$$\frac{2 \sqrt{2} i \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{5} \\ \frac{6}{5} \end{matrix}\middle| {\frac{9}{8}} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$
2*i*sqrt(2)*gamma(1/5)*hyper((-1/2, 1/5), (6/5,), 9/8)/(5*gamma(6/5))
Respuesta numérica
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(0.0154116685964716 + 2.47396363867794j)
(0.0154116685964716 + 2.47396363867794j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.