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