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