Sr Examen

Otras calculadoras

Resolución de integrales/ |x-1|/ |x-1|^n

Integral de |x-1|^n dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2            
  /            
 |             
 |         n   
 |  |x - 1|  dx
 |             
/              
-2
∫−22∣x−1∣n dx\int\limits_{-2}^{2} \left|{x - 1}\right|^{n}\, dx 
Integral(|x - 1|^n, (x, -2, 2))
Respuesta (Indefinida) [src] 
                     //               n                           /pi*n\                         n                           /pi*n\                  \
                     ||      2*(1 - x) *Gamma(-n)*Gamma(1 + n)*sin|----|              2*x*(1 - x) *Gamma(-n)*Gamma(1 + n)*sin|----|                  |
                     ||                                           \ 2  /                                                     \ 2  /                  |
                     ||------------------------------------------------------- - -------------------------------------------------------  for |x| < 1|
  /                  ||     /1   n\      /1   n\          /1   n\      /1   n\        /1   n\      /1   n\          /1   n\      /1   n\             |
 |                   ||Gamma|- + -|*Gamma|- - -| + n*Gamma|- + -|*Gamma|- - -|   Gamma|- + -|*Gamma|- - -| + n*Gamma|- + -|*Gamma|- - -|             |
 |        n          ||     \2   2/      \2   2/          \2   2/      \2   2/        \2   2/      \2   2/          \2   2/      \2   2/             |
 | |x - 1|  dx = C + |<                                                                                                                              |
 |                   ||                                                   /           3   n   |  \                                                   |
/                    ||                                                   |2 + n, 1   - + -   |  |                                                   |
                     ||                                            __1, 2 |           2   2   |  |    /pi*n\                                         |
                     ||                           -2*Gamma(1 + n)*/__     |                   | x|*sin|----|                               otherwise |
                     ||                                           \_|3, 3 |          3   n    |  |    \ 2  /                                         |
                     ||                                                   |   1      - + -, 0 |  |                                                   |
                     \\                                                   \          2   2    |  /                                                   /
∫∣x−1∣n dx=C+{−2x(1−x)nsin⁡(πn2)Γ(−n)Γ(n+1)nΓ(12−n2)Γ(n2+12)+Γ(12−n2)Γ(n2+12)+2(1−x)nsin⁡(πn2)Γ(−n)Γ(n+1)nΓ(12−n2)Γ(n2+12)+Γ(12−n2)Γ(n2+12)for ∣x∣<1−2G3,31,2(n+2,1n2+321n2+32,0|x)sin⁡(πn2)Γ(n+1)otherwise\int \left|{x - 1}\right|^{n}\, dx = C + \begin{cases} - \frac{2 x \left(1 - x\right)^{n} \sin{\left(\frac{\pi n}{2} \right)} \Gamma\left(- n\right) \Gamma\left(n + 1\right)}{n \Gamma\left(\frac{1}{2} - \frac{n}{2}\right) \Gamma\left(\frac{n}{2} + \frac{1}{2}\right) + \Gamma\left(\frac{1}{2} - \frac{n}{2}\right) \Gamma\left(\frac{n}{2} + \frac{1}{2}\right)} + \frac{2 \left(1 - x\right)^{n} \sin{\left(\frac{\pi n}{2} \right)} \Gamma\left(- n\right) \Gamma\left(n + 1\right)}{n \Gamma\left(\frac{1}{2} - \frac{n}{2}\right) \Gamma\left(\frac{n}{2} + \frac{1}{2}\right) + \Gamma\left(\frac{1}{2} - \frac{n}{2}\right) \Gamma\left(\frac{n}{2} + \frac{1}{2}\right)} & \text{for}\: \left|{x}\right| < 1 \\- 2 {G_{3, 3}^{1, 2}\left(\begin{matrix} n + 2, 1 & \frac{n}{2} + \frac{3}{2} \\1 & \frac{n}{2} + \frac{3}{2}, 0 \end{matrix} \middle| {x} \right)} \sin{\left(\frac{\pi n}{2} \right)} \Gamma\left(n + 1\right) & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
/         1 + n      1 + n                                   
|  1     3        2*0                                        
|----- + ------ - --------  for And(n > -oo, n < oo, n != -1)
<1 + n   1 + n     1 + n                                     
|                                                            
|           oo                          otherwise            
\
{−2⋅0n+1n+1+3n+1n+1+1n+1for n>−∞∧n<∞∧n≠−1∞otherwise\begin{cases} - \frac{2 \cdot 0^{n + 1}}{n + 1} + \frac{3^{n + 1}}{n + 1} + \frac{1}{n + 1} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq -1 \\\infty & \text{otherwise} \end{cases} 
=
= 
/         1 + n      1 + n                                   
|  1     3        2*0                                        
|----- + ------ - --------  for And(n > -oo, n < oo, n != -1)
<1 + n   1 + n     1 + n                                     
|                                                            
|           oo                          otherwise            
\
{−2⋅0n+1n+1+3n+1n+1+1n+1for n>−∞∧n<∞∧n≠−1∞otherwise\begin{cases} - \frac{2 \cdot 0^{n + 1}}{n + 1} + \frac{3^{n + 1}}{n + 1} + \frac{1}{n + 1} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq -1 \\\infty & \text{otherwise} \end{cases} 
Piecewise((1/(1 + n) + 3^(1 + n)/(1 + n) - 2*0^(1 + n)/(1 + n), (n > -oo)∧(n < oo)∧(Ne(n, -1))), (oo, True))

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

    © Sr Examen – Калькулятор