Sr Examen
Integral de sgrt(1+4x^3) dx
Solución
Ha introducido
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9 / | | __________ | / 3 | \/ 1 + 4*x dx | / 23 -- 10
$$\int\limits_{\frac{23}{10}}^{9} \sqrt{4 x^{3} + 1}\, dx$$
Integral(sqrt(1 + 4*x^3), (x, 23/10, 9))
Respuesta (Indefinida)
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/ _ | |_ /-1/2, 1/3 | 3 pi*I\ | __________ x*Gamma(1/3)* | | | 4*x *e | | / 3 2 1 \ 4/3 | / | \/ 1 + 4*x dx = C + ------------------------------------------ | 3*Gamma(4/3) /
$$\int \sqrt{4 x^{3} + 1}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {4 x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$
Gráfica
Respuesta
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_ _ / | pi*I\
|_ /-1/2, 1/3 | pi*I\ |_ |-1/2, 1/3 | 12167*e |
3*Gamma(1/3)* | | | 2916*e | 23*Gamma(1/3)* | | | -----------|
2 1 \ 4/3 | / 2 1 \ 4/3 | 250 /
------------------------------------------ - --------------------------------------------
Gamma(4/3) 30*Gamma(4/3)
$$- \frac{23 \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{12167 e^{i \pi}}{250}} \right)}}{30 \Gamma\left(\frac{4}{3}\right)} + \frac{3 \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {2916 e^{i \pi}} \right)}}{\Gamma\left(\frac{4}{3}\right)}$$
=
=
_ _ / | pi*I\
|_ /-1/2, 1/3 | pi*I\ |_ |-1/2, 1/3 | 12167*e |
3*Gamma(1/3)* | | | 2916*e | 23*Gamma(1/3)* | | | -----------|
2 1 \ 4/3 | / 2 1 \ 4/3 | 250 /
------------------------------------------ - --------------------------------------------
Gamma(4/3) 30*Gamma(4/3)
$$- \frac{23 \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{12167 e^{i \pi}}{250}} \right)}}{30 \Gamma\left(\frac{4}{3}\right)} + \frac{3 \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {2916 e^{i \pi}} \right)}}{\Gamma\left(\frac{4}{3}\right)}$$
3*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), 2916*exp_polar(pi*i))/gamma(4/3) - 23*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), 12167*exp_polar(pi*i)/250)/(30*gamma(4/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.