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