Sr Examen
Integral de (√xlnx)^3 dx
Solución
Ha introducido
[src]
1 / | | 3 | / ___ \ | \\/ x *log(x)/ dx | / 0
$$\int\limits_{0}^{1} \left(\sqrt{x} \log{\left(x \right)}\right)^{3}\, dx$$
Integral((sqrt(x)*log(x))^3, (x, 0, 1))
Respuesta (Indefinida)
[src]
// 5/2 5/2 2 5/2 3 5/2 \
|| 96*x 12*x *log (x) 2*x *log (x) 48*x *log(x) |
|| - ------- - --------------- + -------------- + -------------- for |x| < 1|
/ || 625 25 5 125 |
| || |
| 3 || 5/2 /1\ 5/2 2/1\ 5/2 3/1\ |
| / ___ \ || 5/2 48*x *log|-| 12*x *log |-| 2*x *log |-| |
| \\/ x *log(x)/ dx = C + |< 96*x \x/ \x/ \x/ 1 |
| || - ------- - -------------- - --------------- - -------------- for --- < 1|
/ || 625 125 25 5 |x| |
|| |
|| __4, 1 / 1 7/2, 7/2, 7/2, 7/2 | \ __0, 5 /7/2, 7/2, 7/2, 7/2, 1 | \ |
||- 6*/__ | | x| + 6*/__ | | x| otherwise |
|| \_|5, 5 \5/2, 5/2, 5/2, 5/2 0 | / \_|5, 5 \ 5/2, 5/2, 5/2, 5/2, 0 | / |
\\ /
$$\int \left(\sqrt{x} \log{\left(x \right)}\right)^{3}\, dx = C + \begin{cases} \frac{2 x^{\frac{5}{2}} \log{\left(x \right)}^{3}}{5} - \frac{12 x^{\frac{5}{2}} \log{\left(x \right)}^{2}}{25} + \frac{48 x^{\frac{5}{2}} \log{\left(x \right)}}{125} - \frac{96 x^{\frac{5}{2}}}{625} & \text{for}\: \left|{x}\right| < 1 \\- \frac{2 x^{\frac{5}{2}} \log{\left(\frac{1}{x} \right)}^{3}}{5} - \frac{12 x^{\frac{5}{2}} \log{\left(\frac{1}{x} \right)}^{2}}{25} - \frac{48 x^{\frac{5}{2}} \log{\left(\frac{1}{x} \right)}}{125} - \frac{96 x^{\frac{5}{2}}}{625} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- 6 {G_{5, 5}^{4, 1}\left(\begin{matrix} 1 & \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2} \\\frac{5}{2}, \frac{5}{2}, \frac{5}{2}, \frac{5}{2} & 0 \end{matrix} \middle| {x} \right)} + 6 {G_{5, 5}^{0, 5}\left(\begin{matrix} \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 1 & \\ & \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, \frac{5}{2}, 0 \end{matrix} \middle| {x} \right)} & \text{otherwise} \end{cases}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.