Sr Examen

Otras calculadoras

Resolución de integrales/ √xlnx/ (√xlnx)^3

Integral de (√xlnx)^3 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |                3   
 |  /  ___       \    
 |  \\/ x *log(x)/  dx
 |                    
/                     
0
∫01(xlog⁡(x))3 dx\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 |  /             |
                            \\                                                                                                                                    /
∫(xlog⁡(x))3 dx=C+{2x52log⁡(x)35−12x52log⁡(x)225+48x52log⁡(x)125−96x52625for ∣x∣<1−2x52log⁡(1x)35−12x52log⁡(1x)225−48x52log⁡(1x)125−96x52625for 1∣x∣<1−6G5,54,1(172,72,72,7252,52,52,520|x)+6G5,50,5(72,72,72,72,152,52,52,52,0|x)otherwise\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}
Simplificar
Respuesta numérica [src] 
-0.1536
-0.1536

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор