Sr Examen
Integral de x/(sqrt(x+x^3)) dx
Solución
Ha introducido
[src]
1 / | | x | ----------- dx | ________ | / 3 | \/ x + x | / 1/5
$$\int\limits_{\frac{1}{5}}^{1} \frac{x}{\sqrt{x^{3} + x}}\, dx$$
Integral(x/sqrt(x + x^3), (x, 1/5, 1))
Respuesta (Indefinida)
[src]
/ / | | | x | x | ----------- dx = C + | --------------- dx | ________ | ____________ | / 3 | / / 2\ | \/ x + x | \/ x*\1 + x / | | / /
$$\int \frac{x}{\sqrt{x^{3} + x}}\, dx = C + \int \frac{x}{\sqrt{x \left(x^{2} + 1\right)}}\, dx$$
Respuesta
[src]
_ _
|_ /1/2, 3/4 | \ ___ |_ /1/2, 3/4 | \
Gamma(3/4)* | | | -1| \/ 5 *Gamma(3/4)* | | | -1/25|
2 1 \ 7/4 | / 2 1 \ 7/4 | /
------------------------------- - ----------------------------------------
2*Gamma(7/4) 50*Gamma(7/4)
$$\frac{\Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {-1} \right)}}{2 \Gamma\left(\frac{7}{4}\right)} - \frac{\sqrt{5} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {- \frac{1}{25}} \right)}}{50 \Gamma\left(\frac{7}{4}\right)}$$
=
=
_ _
|_ /1/2, 3/4 | \ ___ |_ /1/2, 3/4 | \
Gamma(3/4)* | | | -1| \/ 5 *Gamma(3/4)* | | | -1/25|
2 1 \ 7/4 | / 2 1 \ 7/4 | /
------------------------------- - ----------------------------------------
2*Gamma(7/4) 50*Gamma(7/4)
$$\frac{\Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {-1} \right)}}{2 \Gamma\left(\frac{7}{4}\right)} - \frac{\sqrt{5} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {- \frac{1}{25}} \right)}}{50 \Gamma\left(\frac{7}{4}\right)}$$
gamma(3/4)*hyper((1/2, 3/4), (7/4,), -1)/(2*gamma(7/4)) - sqrt(5)*gamma(3/4)*hyper((1/2, 3/4), (7/4,), -1/25)/(50*gamma(7/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.