Sr Examen
Integral de 1/(sqrt(2*x+1)*(sqrt(sqrt(2*x+1)))) dx
Solución
Ha introducido
[src]
1 / | | 1 | ---------------------------- dx | _____________ | _________ / _________ | \/ 2*x + 1 *\/ \/ 2*x + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{2 x + 1} \sqrt{\sqrt{2 x + 1}}}\, dx$$
Integral(1/(sqrt(2*x + 1)*sqrt(sqrt(2*x + 1))), (x, 0, 1))
Respuesta (Indefinida)
[src]
// 4 ___ 4 _________ \
|| \/ 2 *\/ 1/2 + x *Gamma(1/4) |
/ || ---------------------------- for |1/2 + x| > 0|
| || 2*Gamma(5/4) |
| 1 || |
| ---------------------------- dx = C + |<4 ___ __1, 1 / 1 5/4 | \ 4 ___ __0, 2 /5/4, 1 | \ |
| _____________ ||\/ 2 */__ | | 1/2 + x| \/ 2 */__ | | 1/2 + x| |
| _________ / _________ || \_|2, 2 \1/4 0 | / \_|2, 2 \ 1/4, 0 | / |
| \/ 2*x + 1 *\/ \/ 2*x + 1 ||---------------------------------- + ---------------------------------------- otherwise |
| || 2 2 |
/ \\ /
$$\int \frac{1}{\sqrt{2 x + 1} \sqrt{\sqrt{2 x + 1}}}\, dx = C + \begin{cases} \frac{\sqrt[4]{2} \sqrt[4]{x + \frac{1}{2}} \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} & \text{for}\: \left|{x + \frac{1}{2}}\right| > 0 \\\frac{\sqrt[4]{2} {G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{5}{4} \\\frac{1}{4} & 0 \end{matrix} \middle| {x + \frac{1}{2}} \right)}}{2} + \frac{\sqrt[4]{2} {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{5}{4}, 1 & \\ & \frac{1}{4}, 0 \end{matrix} \middle| {x + \frac{1}{2}} \right)}}{2} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
4 ___ -2 + 2*\/ 3
$$-2 + 2 \sqrt[4]{3}$$
=
=
4 ___ -2 + 2*\/ 3
$$-2 + 2 \sqrt[4]{3}$$
-2 + 2*3^(1/4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.