Sr Examen
Integral de dx/((x^(3/4))*(x^(2/3))) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------- dx | 3/4 2/3 | x *x | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{\frac{2}{3}} x^{\frac{3}{4}}}\, dx$$
Integral(1/(x^(3/4)*x^(2/3)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// Gamma(-5/12) \ / || ----------------- for Or(|x| > 1, |x| < 1)| | || 5/12 | | 1 || x *Gamma(7/12) | | --------- dx = C + |< | | 3/4 2/3 || __1, 1 / 1 7/12 | \ __0, 2 /7/12, 1 | \ | | x *x ||/__ | | x| + /__ | | x| otherwise | | ||\_|2, 2 \-5/12 0 | / \_|2, 2 \ -5/12, 0 | / | / \\ /
$$\int \frac{1}{x^{\frac{2}{3}} x^{\frac{3}{4}}}\, dx = C + \begin{cases} \frac{\Gamma\left(- \frac{5}{12}\right)}{x^{\frac{5}{12}} \Gamma\left(\frac{7}{12}\right)} & \text{for}\: \left|{x}\right| > 1 \vee \left|{x}\right| < 1 \\{G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{7}{12} \\- \frac{5}{12} & 0 \end{matrix} \middle| {x} \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{7}{12}, 1 & \\ & - \frac{5}{12}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.