Sr Examen
Integral de sqrt(5x^4+3) dx
Solución
Ha introducido
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1 / | | __________ | / 4 | \/ 5*x + 3 dx | / 0
$$\int\limits_{0}^{1} \sqrt{5 x^{4} + 3}\, dx$$
Integral(sqrt(5*x^4 + 3), (x, 0, 1))
Respuesta (Indefinida)
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/ _ / | 4 pi*I\ | ___ |_ |-1/2, 1/4 | 5*x *e | | __________ x*\/ 3 *Gamma(1/4)* | | | ----------| | / 4 2 1 \ 5/4 | 3 / | \/ 5*x + 3 dx = C + ------------------------------------------------ | 4*Gamma(5/4) /
$$\int \sqrt{5 x^{4} + 3}\, dx = C + \frac{\sqrt{3} x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{5 x^{4} e^{i \pi}}{3}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta
[src]
_ / | pi*I\
___ |_ |-1/2, 1/4 | 5*e |
\/ 3 *Gamma(1/4)* | | | -------|
2 1 \ 5/4 | 3 /
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4*Gamma(5/4)
$$\frac{\sqrt{3} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{5 e^{i \pi}}{3}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
=
=
_ / | pi*I\
___ |_ |-1/2, 1/4 | 5*e |
\/ 3 *Gamma(1/4)* | | | -------|
2 1 \ 5/4 | 3 /
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4*Gamma(5/4)
$$\frac{\sqrt{3} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {\frac{5 e^{i \pi}}{3}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
sqrt(3)*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 5*exp_polar(pi*i)/3)/(4*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.