Sr Examen
Integral de sqrt(1+((x-1)^3)^2) dx
Solución
Ha introducido
[src]
5 / | | _________________ | / 2 | / / 3\ | \/ 1 + \(x - 1) / dx | / 2
$$\int\limits_{2}^{5} \sqrt{\left(\left(x - 1\right)^{3}\right)^{2} + 1}\, dx$$
Integral(sqrt(1 + ((x - 1)^3)^2), (x, 2, 5))
Respuesta (Indefinida)
[src]
/ | _ | _________________ |_ /-1/2, 1/6 | 6 pi*I\ | / 2 (-1 + x)*Gamma(1/6)* | | | (-1 + x) *e | | / / 3\ 2 1 \ 7/6 | / | \/ 1 + \(x - 1) / dx = C + ------------------------------------------------------ | 6*Gamma(7/6) /
$$\int \sqrt{\left(\left(x - 1\right)^{3}\right)^{2} + 1}\, dx = C + \frac{\left(x - 1\right) \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {\left(x - 1\right)^{6} e^{i \pi}} \right)}}{6 \Gamma\left(\frac{7}{6}\right)}$$
Gráfica
Respuesta
[src]
_ _
|_ /-1/2, 1/6 | \ |_ /-1/2, 1/6 | pi*I\
Gamma(1/6)* | | | -1| 2*Gamma(1/6)* | | | 4096*e |
2 1 \ 7/6 | / 2 1 \ 7/6 | /
- -------------------------------- + ------------------------------------------
6*Gamma(7/6) 3*Gamma(7/6)
$$- \frac{\Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {-1} \right)}}{6 \Gamma\left(\frac{7}{6}\right)} + \frac{2 \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {4096 e^{i \pi}} \right)}}{3 \Gamma\left(\frac{7}{6}\right)}$$
=
=
_ _
|_ /-1/2, 1/6 | \ |_ /-1/2, 1/6 | pi*I\
Gamma(1/6)* | | | -1| 2*Gamma(1/6)* | | | 4096*e |
2 1 \ 7/6 | / 2 1 \ 7/6 | /
- -------------------------------- + ------------------------------------------
6*Gamma(7/6) 3*Gamma(7/6)
$$- \frac{\Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {-1} \right)}}{6 \Gamma\left(\frac{7}{6}\right)} + \frac{2 \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {4096 e^{i \pi}} \right)}}{3 \Gamma\left(\frac{7}{6}\right)}$$
-gamma(1/6)*hyper((-1/2, 1/6), (7/6,), -1)/(6*gamma(7/6)) + 2*gamma(1/6)*hyper((-1/2, 1/6), (7/6,), 4096*exp_polar(pi*i))/(3*gamma(7/6))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.