Sr Examen
Integral de 4*x*d*x/(sqrt(3-x^4)) dx
Solución
Ha introducido
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1 / | | 4*x*d*x | ----------- dx | ________ | / 4 | \/ 3 - x | / 0
$$\int\limits_{0}^{1} \frac{x d 4 x}{\sqrt{3 - x^{4}}}\, dx$$
Integral((((4*x)*d)*x)/sqrt(3 - x^4), (x, 0, 1))
Respuesta (Indefinida)
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_ / | 4 2*pi*I\
/ ___ 3 |_ |1/2, 3/4 | x *e |
| d*\/ 3 *x *Gamma(3/4)* | | | ----------|
| 4*x*d*x 2 1 \ 7/4 | 3 /
| ----------- dx = C + --------------------------------------------------
| ________ 3*Gamma(7/4)
| / 4
| \/ 3 - x
|
/
$$\int \frac{x d 4 x}{\sqrt{3 - x^{4}}}\, dx = C + \frac{\sqrt{3} d x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{3}} \right)}}{3 \Gamma\left(\frac{7}{4}\right)}$$
Respuesta
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_
___ |_ /1/2, 3/4 | \
d*\/ 3 *Gamma(3/4)* | | | 1/3|
2 1 \ 7/4 | /
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3*Gamma(7/4)
$$\frac{\sqrt{3} d \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{1}{3}} \right)}}{3 \Gamma\left(\frac{7}{4}\right)}$$
=
=
_
___ |_ /1/2, 3/4 | \
d*\/ 3 *Gamma(3/4)* | | | 1/3|
2 1 \ 7/4 | /
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3*Gamma(7/4)
$$\frac{\sqrt{3} d \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {\frac{1}{3}} \right)}}{3 \Gamma\left(\frac{7}{4}\right)}$$
d*sqrt(3)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), 1/3)/(3*gamma(7/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.