Sr Examen
Integral de 1/(x*(log(2)x)^(1/5)) dx
Solución
Ha introducido
[src]
32 / | | 1 | -------------- dx | 5 __________ | x*\/ log(2)*x | / 1
$$\int\limits_{1}^{32} \frac{1}{x \sqrt[5]{x \log{\left(2 \right)}}}\, dx$$
Integral(1/(x*(log(2)*x)^(1/5)), (x, 1, 32))
Respuesta (Indefinida)
[src]
// Gamma(-1/5) \
|| --------------------------- for Or(|x| > 1, |x| < 1)|
/ || 5 ___ 5 ________ |
| || \/ x *Gamma(4/5)*\/ log(2) |
| 1 || |
| -------------- dx = C + |< __1, 1 / 1 4/5 | \ __0, 2 /4/5, 1 | \ |
| 5 __________ ||/__ | | x| /__ | | x| |
| x*\/ log(2)*x ||\_|2, 2 \-1/5 0 | / \_|2, 2 \ -1/5, 0 | / |
| ||----------------------- + ----------------------------- otherwise |
/ || 5 ________ 5 ________ |
\\ \/ log(2) \/ log(2) /
$$\int \frac{1}{x \sqrt[5]{x \log{\left(2 \right)}}}\, dx = C + \begin{cases} \frac{\Gamma\left(- \frac{1}{5}\right)}{\sqrt[5]{x} \sqrt[5]{\log{\left(2 \right)}} \Gamma\left(\frac{4}{5}\right)} & \text{for}\: \left|{x}\right| > 1 \vee \left|{x}\right| < 1 \\\frac{{G_{2, 2}^{1, 1}\left(\begin{matrix} 1 & \frac{4}{5} \\- \frac{1}{5} & 0 \end{matrix} \middle| {x} \right)}}{\sqrt[5]{\log{\left(2 \right)}}} + \frac{{G_{2, 2}^{0, 2}\left(\begin{matrix} \frac{4}{5}, 1 & \\ & - \frac{1}{5}, 0 \end{matrix} \middle| {x} \right)}}{\sqrt[5]{\log{\left(2 \right)}}} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
5 ------------ 5 ________ 2*\/ log(2)
$$\frac{5}{2 \sqrt[5]{\log{\left(2 \right)}}}$$
=
=
5 ------------ 5 ________ 2*\/ log(2)
$$\frac{5}{2 \sqrt[5]{\log{\left(2 \right)}}}$$
5/(2*log(2)^(1/5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.