Sr Examen
Integral de 1/(sqrt(x^3+1)) dx
Solución
Ha introducido
[src]
oo / | | 1 | ----------- dx | ________ | / 3 | \/ x + 1 | / 3
$$\int\limits_{3}^{\infty} \frac{1}{\sqrt{x^{3} + 1}}\, dx$$
Integral(1/(sqrt(x^3 + 1)), (x, 3, oo))
Respuesta (Indefinida)
[src]
_ / |_ /1/3, 1/2 | 3 pi*I\ | x*Gamma(1/3)* | | | x *e | | 1 2 1 \ 4/3 | / | ----------- dx = C + --------------------------------------- | ________ 3*Gamma(4/3) | / 3 | \/ x + 1 | /
$$\int \frac{1}{\sqrt{x^{3} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
Respuesta
[src]
_
___ |_ /1/6, 1/2 | \
\/ 3 *Gamma(1/6)* | | | -1/27|
2 1 \ 7/6 | /
----------------------------------------
9*Gamma(7/6)
$$\frac{\sqrt{3} \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6} \end{matrix}\middle| {- \frac{1}{27}} \right)}}{9 \Gamma\left(\frac{7}{6}\right)}$$
=
=
_
___ |_ /1/6, 1/2 | \
\/ 3 *Gamma(1/6)* | | | -1/27|
2 1 \ 7/6 | /
----------------------------------------
9*Gamma(7/6)
$$\frac{\sqrt{3} \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6} \end{matrix}\middle| {- \frac{1}{27}} \right)}}{9 \Gamma\left(\frac{7}{6}\right)}$$
sqrt(3)*gamma(1/6)*hyper((1/6, 1/2), (7/6,), -1/27)/(9*gamma(7/6))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.