Integral de e^(3*x)*log(x)/x dx
Solución
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 | / |
\\ /
∫xe3xlog(x)dx=C−⎩⎨⎧3x3F3(1,1,12,2,23x)+2log(x)2+γlog(x)+log(3)log(x)3x3F3(1,1,12,2,23x)+iπlog(x1)+2log(x)2+γlog(x)+log(3)log(x)+iπlog(x)3x3F3(1,1,12,2,23x)+iπG2,22,0(0,01,1x)−iπG2,20,2(1,10,0x)+2log(x)2+γlog(x)+log(3)log(x)+iπlog(x)for∣x∣<1for∣x∣1<1otherwise+log(x)Ei(3x)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.