Sr Examen
Integral de e^(3*x)*log(x)/x dx
Solución
Ha introducido
[src]
1 / | | 3*x | E *log(x) | ----------- dx | x | / 0
$$\int\limits_{0}^{1} \frac{e^{3 x} \log{\left(x \right)}}{x}\, dx$$
Integral((E^(3*x)*log(x))/x, (x, 0, 1))
Respuesta (Indefinida)
[src]
// 2 _ \
|| log (x) |_ /1, 1, 1 | \ |
|| ------- + EulerGamma*log(x) + log(3)*log(x) + 3*x* | | | 3*x| for |x| < 1|
/ || 2 3 3 \2, 2, 2 | / |
| || |
| 3*x || 2 _ |
| E *log(x) || log (x) |_ /1, 1, 1 | \ /1\ 1 |
| ----------- dx = C - |< ------- + EulerGamma*log(x) + log(3)*log(x) + 3*x* | | | 3*x| + pi*I*log(x) + pi*I*log|-| for --- < 1| + Ei(3*x)*log(x)
| x || 2 3 3 \2, 2, 2 | / \x/ |x| |
| || |
/ || 2 _ |
||log (x) |_ /1, 1, 1 | \ __2, 0 / 1, 1 | \ __0, 2 /1, 1 | \ |
||------- + EulerGamma*log(x) + log(3)*log(x) + 3*x* | | | 3*x| + pi*I*log(x) + pi*I*/__ | | x| - pi*I*/__ | | x| otherwise |
|| 2 3 3 \2, 2, 2 | / \_|2, 2 \0, 0 | / \_|2, 2 \ 0, 0 | / |
\\ /
$$\int \frac{e^{3 x} \log{\left(x \right)}}{x}\, dx = C - \begin{cases} 3 x {{}_{3}F_{3}\left(\begin{matrix} 1, 1, 1 \\ 2, 2, 2 \end{matrix}\middle| {3 x} \right)} + \frac{\log{\left(x \right)}^{2}}{2} + \gamma \log{\left(x \right)} + \log{\left(3 \right)} \log{\left(x \right)} & \text{for}\: \left|{x}\right| < 1 \\3 x {{}_{3}F_{3}\left(\begin{matrix} 1, 1, 1 \\ 2, 2, 2 \end{matrix}\middle| {3 x} \right)} + i \pi \log{\left(\frac{1}{x} \right)} + \frac{\log{\left(x \right)}^{2}}{2} + \gamma \log{\left(x \right)} + \log{\left(3 \right)} \log{\left(x \right)} + i \pi \log{\left(x \right)} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\3 x {{}_{3}F_{3}\left(\begin{matrix} 1, 1, 1 \\ 2, 2, 2 \end{matrix}\middle| {3 x} \right)} + i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x} \right)} - i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x} \right)} + \frac{\log{\left(x \right)}^{2}}{2} + \gamma \log{\left(x \right)} + \log{\left(3 \right)} \log{\left(x \right)} + i \pi \log{\left(x \right)} & \text{otherwise} \end{cases} + \log{\left(x \right)} \operatorname{Ei}{\left(3 x \right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.