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Simplificación de expresiones/ Descomposición en fracciones simples/ log(y-1)^2+2*log(2/(y-1))*(y+log(y-1))+2*log(y-1)+log(2/(y-1))^2*y+2*y

¿Cómo vas a descomponer esta log(y-1)^2+2*log(2/(y-1))*(y+log(y-1))+2*log(y-1)+log(2/(y-1))^2*y+2*y expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   2               /  2  \                                      2/  2  \        
log (y - 1) + 2*log|-----|*(y + log(y - 1)) + 2*log(y - 1) + log |-----|*y + 2*y
                   \y - 1/                                       \y - 1/
2y+(ylog⁡(2y−1)2+(((y+log⁡(y−1))2log⁡(2y−1)+log⁡(y−1)2)+2log⁡(y−1)))2 y + \left(y \log{\left(\frac{2}{y - 1} \right)}^{2} + \left(\left(\left(y + \log{\left(y - 1 \right)}\right) 2 \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2}\right) + 2 \log{\left(y - 1 \right)}\right)\right) 
log(y - 1)^2 + (2*log(2/(y - 1)))*(y + log(y - 1)) + 2*log(y - 1) + log(2/(y - 1))^2*y + 2*y
Simplificación general [src] 
   2                                      2/  2   \                          /  2   \
log (-1 + y) + 2*y + 2*log(-1 + y) + y*log |------| + 2*(y + log(-1 + y))*log|------|
                                           \-1 + y/                          \-1 + y/
ylog⁡(2y−1)2+2y+2(y+log⁡(y−1))log⁡(2y−1)+log⁡(y−1)2+2log⁡(y−1)y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)} 
log(-1 + y)^2 + 2*y + 2*log(-1 + y) + y*log(2/(-1 + y))^2 + 2*(y + log(-1 + y))*log(2/(-1 + y))
Parte trigonométrica [src] 
   2                                      2/  2   \                          /  2   \
log (-1 + y) + 2*y + 2*log(-1 + y) + y*log |------| + 2*(y + log(-1 + y))*log|------|
                                           \-1 + y/                          \-1 + y/
ylog⁡(2y−1)2+2y+2(y+log⁡(y−1))log⁡(2y−1)+log⁡(y−1)2+2log⁡(y−1)y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)} 
log(-1 + y)^2 + 2*y + 2*log(-1 + y) + y*log(2/(-1 + y))^2 + 2*(y + log(-1 + y))*log(2/(-1 + y))
Respuesta numérica [src] 
log(y - 1)^2 + 2.0*y + 2.0*log(y - 1) + y*log(2/(y - 1))^2 + 2.0*(y + log(y - 1))*log(2/(y - 1))
log(y - 1)^2 + 2.0*y + 2.0*log(y - 1) + y*log(2/(y - 1))^2 + 2.0*(y + log(y - 1))*log(2/(y - 1))
Denominador común [src] 
   2                                      2           2/  1   \                       /  1   \                               /  1   \                             /  1   \
log (-1 + y) + 2*y + 2*log(-1 + y) + y*log (2) + y*log |------| + 2*y*log(2) + 2*y*log|------| + 2*log(2)*log(-1 + y) + 2*log|------|*log(-1 + y) + 2*y*log(2)*log|------|
                                                       \-1 + y/                       \-1 + y/                               \-1 + y/                             \-1 + y/
ylog⁡(1y−1)2+2ylog⁡(2)log⁡(1y−1)+2ylog⁡(1y−1)+ylog⁡(2)2+2ylog⁡(2)+2y+2log⁡(1y−1)log⁡(y−1)+log⁡(y−1)2+2log⁡(2)log⁡(y−1)+2log⁡(y−1)y \log{\left(\frac{1}{y - 1} \right)}^{2} + 2 y \log{\left(2 \right)} \log{\left(\frac{1}{y - 1} \right)} + 2 y \log{\left(\frac{1}{y - 1} \right)} + y \log{\left(2 \right)}^{2} + 2 y \log{\left(2 \right)} + 2 y + 2 \log{\left(\frac{1}{y - 1} \right)} \log{\left(y - 1 \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(y - 1 \right)} + 2 \log{\left(y - 1 \right)} 
log(-1 + y)^2 + 2*y + 2*log(-1 + y) + y*log(2)^2 + y*log(1/(-1 + y))^2 + 2*y*log(2) + 2*y*log(1/(-1 + y)) + 2*log(2)*log(-1 + y) + 2*log(1/(-1 + y))*log(-1 + y) + 2*y*log(2)*log(1/(-1 + y))
Denominador racional [src] 
   2                                      2/  2  \          /  2  \        /  2  \            
log (-1 + y) + 2*y + 2*log(-1 + y) + y*log |-----| + 2*y*log|-----| + 2*log|-----|*log(-1 + y)
                                           \y - 1/          \y - 1/        \y - 1/
ylog⁡(2y−1)2+2ylog⁡(2y−1)+2y+2log⁡(2y−1)log⁡(y−1)+log⁡(y−1)2+2log⁡(y−1)y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y \log{\left(\frac{2}{y - 1} \right)} + 2 y + 2 \log{\left(\frac{2}{y - 1} \right)} \log{\left(y - 1 \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)} 
log(-1 + y)^2 + 2*y + 2*log(-1 + y) + y*log(2/(y - 1))^2 + 2*y*log(2/(y - 1)) + 2*log(2/(y - 1))*log(-1 + y)
Potencias [src] 
   2                                      2/  2   \                          /  2   \
log (-1 + y) + 2*y + 2*log(-1 + y) + y*log |------| + 2*(y + log(-1 + y))*log|------|
                                           \-1 + y/                          \-1 + y/
ylog⁡(2y−1)2+2y+2(y+log⁡(y−1))log⁡(2y−1)+log⁡(y−1)2+2log⁡(y−1)y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)} 
log(-1 + y)^2 + 2*y + 2*log(-1 + y) + y*log(2/(-1 + y))^2 + 2*(y + log(-1 + y))*log(2/(-1 + y))
Unión de expresiones racionales [src] 
   2                                      2/  2   \                          /  2   \
log (-1 + y) + 2*y + 2*log(-1 + y) + y*log |------| + 2*(y + log(-1 + y))*log|------|
                                           \-1 + y/                          \-1 + y/
ylog⁡(2y−1)2+2y+2(y+log⁡(y−1))log⁡(2y−1)+log⁡(y−1)2+2log⁡(y−1)y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)} 
log(-1 + y)^2 + 2*y + 2*log(-1 + y) + y*log(2/(-1 + y))^2 + 2*(y + log(-1 + y))*log(2/(-1 + y))
Combinatoria [src] 
   2                                      2           2/  1   \                       /  1   \                               /  1   \                             /  1   \
log (-1 + y) + 2*y + 2*log(-1 + y) + y*log (2) + y*log |------| + 2*y*log(2) + 2*y*log|------| + 2*log(2)*log(-1 + y) + 2*log|------|*log(-1 + y) + 2*y*log(2)*log|------|
                                                       \-1 + y/                       \-1 + y/                               \-1 + y/                             \-1 + y/
ylog⁡(1y−1)2+2ylog⁡(2)log⁡(1y−1)+2ylog⁡(1y−1)+ylog⁡(2)2+2ylog⁡(2)+2y+2log⁡(1y−1)log⁡(y−1)+log⁡(y−1)2+2log⁡(2)log⁡(y−1)+2log⁡(y−1)y \log{\left(\frac{1}{y - 1} \right)}^{2} + 2 y \log{\left(2 \right)} \log{\left(\frac{1}{y - 1} \right)} + 2 y \log{\left(\frac{1}{y - 1} \right)} + y \log{\left(2 \right)}^{2} + 2 y \log{\left(2 \right)} + 2 y + 2 \log{\left(\frac{1}{y - 1} \right)} \log{\left(y - 1 \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(y - 1 \right)} + 2 \log{\left(y - 1 \right)} 
log(-1 + y)^2 + 2*y + 2*log(-1 + y) + y*log(2)^2 + y*log(1/(-1 + y))^2 + 2*y*log(2) + 2*y*log(1/(-1 + y)) + 2*log(2)*log(-1 + y) + 2*log(1/(-1 + y))*log(-1 + y) + 2*y*log(2)*log(1/(-1 + y))
Compilar la expresión [src] 
   2                                    2/  2  \                         /  2  \
log (y - 1) + 2*y + 2*log(y - 1) + y*log |-----| + 2*(y + log(y - 1))*log|-----|
                                         \y - 1/                         \y - 1/
ylog⁡(2y−1)2+2y+2(y+log⁡(y−1))log⁡(2y−1)+log⁡(y−1)2+2log⁡(y−1)y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)} 
log(y - 1)^2 + 2*y + 2*log(y - 1) + y*log(2/(y - 1))^2 + 2*(y + log(y - 1))*log(2/(y - 1))
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