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Resolución de integrales/ 2*x-1/ (x-1)/ (x-1)/(t^22*x-1)

Integral de (x-1)/(t^22*x-1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1             
  /             
 |              
 |    x - 1     
 |  --------- dx
 |   22         
 |  t  *x - 1   
 |              
/               
0
∫01x−1t22x−1 dx\int\limits_{0}^{1} \frac{x - 1}{t^{22} x - 1}\, dx 
Integral((x - 1)/(t^22*x - 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                                                                                                                         //                      22    \
                                                                                                                                                         ||      -x         for t   = 0|
                                                                                                                                                         ||                            |
                                             /         2    3    4    5    6    7    8    9    10\ /     2    4    6    8    10        3    5    7    9\ ||   /        22\             |
                            (1 + t)*(-1 + t)*\1 + t + t  + t  + t  + t  + t  + t  + t  + t  + t  /*\1 + t  + t  + t  + t  + t   - t - t  - t  - t  - t /*|
∫x−1t22x−1 dx=C+xt22−(t−1)(t+1)(t10−t9+t8−t7+t6−t5+t4−t3+t2−t+1)(t10+t9+t8+t7+t6+t5+t4+t3+t2+t+1)({−xfor t22=0log⁡(t22x−1)t22otherwise)t22\int \frac{x - 1}{t^{22} x - 1}\, dx = C + \frac{x}{t^{22}} - \frac{\left(t - 1\right) \left(t + 1\right) \left(t^{10} - t^{9} + t^{8} - t^{7} + t^{6} - t^{5} + t^{4} - t^{3} + t^{2} - t + 1\right) \left(t^{10} + t^{9} + t^{8} + t^{7} + t^{6} + t^{5} + t^{4} + t^{3} + t^{2} + t + 1\right) \left(\begin{cases} - x & \text{for}\: t^{22} = 0 \\\frac{\log{\left(t^{22} x - 1 \right)}}{t^{22}} & \text{otherwise} \end{cases}\right)}{t^{22}}
Simplificar
Respuesta [src] 
                       /         2    3    4    5    6    7    8    9    10\ /     2    4    6    8    10        3    5    7    9\    /      22\                         /         2    3    4    5    6    7    8    9    10\ /     2    4    6    8    10        3    5    7    9\
 1    (1 + t)*(-1 + t)*\1 + t + t  + t  + t  + t  + t  + t  + t  + t  + t  /*\1 + t  + t  + t  + t  + t   - t - t  - t  - t  - t /*log\-1 + t  /   pi*I*(1 + t)*(-1 + t)*\1 + t + t  + t  + t  + t  + t  + t  + t  + t  + t  /*\1 + t  + t  + t  + t  + t   - t - t  - t  - t  - t /
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 22                                                                       44                                                                                                                                       44                                                               
t                                                                        t                                                                                                                                        t
1t22−(t−1)(t+1)(t10−t9+t8−t7+t6−t5+t4−t3+t2−t+1)(t10+t9+t8+t7+t6+t5+t4+t3+t2+t+1)log⁡(t22−1)t44+iπ(t−1)(t+1)(t10−t9+t8−t7+t6−t5+t4−t3+t2−t+1)(t10+t9+t8+t7+t6+t5+t4+t3+t2+t+1)t44\frac{1}{t^{22}} - \frac{\left(t - 1\right) \left(t + 1\right) \left(t^{10} - t^{9} + t^{8} - t^{7} + t^{6} - t^{5} + t^{4} - t^{3} + t^{2} - t + 1\right) \left(t^{10} + t^{9} + t^{8} + t^{7} + t^{6} + t^{5} + t^{4} + t^{3} + t^{2} + t + 1\right) \log{\left(t^{22} - 1 \right)}}{t^{44}} + \frac{i \pi \left(t - 1\right) \left(t + 1\right) \left(t^{10} - t^{9} + t^{8} - t^{7} + t^{6} - t^{5} + t^{4} - t^{3} + t^{2} - t + 1\right) \left(t^{10} + t^{9} + t^{8} + t^{7} + t^{6} + t^{5} + t^{4} + t^{3} + t^{2} + t + 1\right)}{t^{44}} 
=
= 
                       /         2    3    4    5    6    7    8    9    10\ /     2    4    6    8    10        3    5    7    9\    /      22\                         /         2    3    4    5    6    7    8    9    10\ /     2    4    6    8    10        3    5    7    9\
 1    (1 + t)*(-1 + t)*\1 + t + t  + t  + t  + t  + t  + t  + t  + t  + t  /*\1 + t  + t  + t  + t  + t   - t - t  - t  - t  - t /*log\-1 + t  /   pi*I*(1 + t)*(-1 + t)*\1 + t + t  + t  + t  + t  + t  + t  + t  + t  + t  /*\1 + t  + t  + t  + t  + t   - t - t  - t  - t  - t /
--- - ------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------
 22                                                                       44                                                                                                                                       44                                                               
t                                                                        t                                                                                                                                        t
1t22−(t−1)(t+1)(t10−t9+t8−t7+t6−t5+t4−t3+t2−t+1)(t10+t9+t8+t7+t6+t5+t4+t3+t2+t+1)log⁡(t22−1)t44+iπ(t−1)(t+1)(t10−t9+t8−t7+t6−t5+t4−t3+t2−t+1)(t10+t9+t8+t7+t6+t5+t4+t3+t2+t+1)t44\frac{1}{t^{22}} - \frac{\left(t - 1\right) \left(t + 1\right) \left(t^{10} - t^{9} + t^{8} - t^{7} + t^{6} - t^{5} + t^{4} - t^{3} + t^{2} - t + 1\right) \left(t^{10} + t^{9} + t^{8} + t^{7} + t^{6} + t^{5} + t^{4} + t^{3} + t^{2} + t + 1\right) \log{\left(t^{22} - 1 \right)}}{t^{44}} + \frac{i \pi \left(t - 1\right) \left(t + 1\right) \left(t^{10} - t^{9} + t^{8} - t^{7} + t^{6} - t^{5} + t^{4} - t^{3} + t^{2} - t + 1\right) \left(t^{10} + t^{9} + t^{8} + t^{7} + t^{6} + t^{5} + t^{4} + t^{3} + t^{2} + t + 1\right)}{t^{44}} 
t^(-22) - (1 + t)*(-1 + t)*(1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10)*(1 + t^2 + t^4 + t^6 + t^8 + t^10 - t - t^3 - t^5 - t^7 - t^9)*log(-1 + t^22)/t^44 + pi*i*(1 + t)*(-1 + t)*(1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10)*(1 + t^2 + t^4 + t^6 + t^8 + t^10 - t - t^3 - t^5 - t^7 - t^9)/t^44

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

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