Sr Examen
Integral de sqrt(7+x^4) dx
Solución
Ha introducido
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___ \/ 3 / | | ________ | / 4 | \/ 7 + x dx | / 1
$$\int\limits_{1}^{\sqrt{3}} \sqrt{x^{4} + 7}\, dx$$
Integral(sqrt(7 + x^4), (x, 1, sqrt(3)))
Respuesta (Indefinida)
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/ _ / | 4 pi*I\ | ___ |_ |-1/2, 1/4 | x *e | | ________ x*\/ 7 *Gamma(1/4)* | | | --------| | / 4 2 1 \ 5/4 | 7 / | \/ 7 + x dx = C + ---------------------------------------------- | 4*Gamma(5/4) /
$$\int \sqrt{x^{4} + 7}\, dx = C + \frac{\sqrt{7} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{x^{4} e^{i \pi}}{7}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta
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_ _ / | pi*I\
___ |_ /-1/2, 1/4 | \ ____ |_ |-1/2, 1/4 | 9*e |
\/ 7 *Gamma(1/4)* | | | -1/7| \/ 21 *Gamma(1/4)* | | | -------|
2 1 \ 5/4 | / 2 1 \ 5/4 | 7 /
- ---------------------------------------- + --------------------------------------------
4*Gamma(5/4) 4*Gamma(5/4)
$$- \frac{\sqrt{7} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {- \frac{1}{7}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{21} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{9 e^{i \pi}}{7}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
=
=
_ _ / | pi*I\
___ |_ /-1/2, 1/4 | \ ____ |_ |-1/2, 1/4 | 9*e |
\/ 7 *Gamma(1/4)* | | | -1/7| \/ 21 *Gamma(1/4)* | | | -------|
2 1 \ 5/4 | / 2 1 \ 5/4 | 7 /
- ---------------------------------------- + --------------------------------------------
4*Gamma(5/4) 4*Gamma(5/4)
$$- \frac{\sqrt{7} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {- \frac{1}{7}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{21} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{9 e^{i \pi}}{7}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
-sqrt(7)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), -1/7)/(4*gamma(5/4)) + sqrt(21)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 9*exp_polar(pi*i)/7)/(4*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.