Sr Examen
Integral de 1/(1+xsqrtx) dx
Solución
Ha introducido
[src]
oo / | | 1 | ----------- dx | ___ | 1 + x*\/ x | / 1
$$\int\limits_{1}^{\infty} \frac{1}{\sqrt{x} x + 1}\, dx$$
Integral(1/(1 + x*sqrt(x)), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ ___ / 1 ___\\
|2*\/ 3 *|- - + \/ x ||
/ ___ | \ 2 /|
| / ___\ / ___\ 2*\/ 3 *atan|---------------------|
| 1 2*log\1 + \/ x / log\1 + x - \/ x / \ 3 /
| ----------- dx = C - ---------------- + ------------------ + -----------------------------------
| ___ 3 3 3
| 1 + x*\/ x
|
/
$$\int \frac{1}{\sqrt{x} x + 1}\, dx = C - \frac{2 \log{\left(\sqrt{x} + 1 \right)}}{3} + \frac{\log{\left(- \sqrt{x} + x + 1 \right)}}{3} + \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(\sqrt{x} - \frac{1}{2}\right)}{3} \right)}}{3}$$
Respuesta
[src]
__2, 5 /2/3, 1/6, 1/3, 2/3, 1 | \
/__ | | 1|
\_|5, 5 \ 2/3, 1/6 0, 1/3, 2/3 | /
------------------------------------------------
3*pi
$$\frac{{G_{5, 5}^{2, 5}\left(\begin{matrix} \frac{2}{3}, \frac{1}{6}, \frac{1}{3}, \frac{2}{3}, 1 & \\\frac{2}{3}, \frac{1}{6} & 0, \frac{1}{3}, \frac{2}{3} \end{matrix} \middle| {1} \right)}}{3 \pi}$$
=
=
__2, 5 /2/3, 1/6, 1/3, 2/3, 1 | \
/__ | | 1|
\_|5, 5 \ 2/3, 1/6 0, 1/3, 2/3 | /
------------------------------------------------
3*pi
$$\frac{{G_{5, 5}^{2, 5}\left(\begin{matrix} \frac{2}{3}, \frac{1}{6}, \frac{1}{3}, \frac{2}{3}, 1 & \\\frac{2}{3}, \frac{1}{6} & 0, \frac{1}{3}, \frac{2}{3} \end{matrix} \middle| {1} \right)}}{3 \pi}$$
meijerg(((2/3, 1/6, 1/3, 2/3, 1), ()), ((2/3, 1/6), (0, 1/3, 2/3)), 1)/(3*pi)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.