Sr Examen
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?
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/
$$2 y + \left(y \log{\left(\frac{2}{y - 1} \right)}^{2} + \left(\left(\left(y + \log{\left(y - 1 \right)}\right) 2 \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2}\right) + 2 \log{\left(y - 1 \right)}\right)\right)$$
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/
$$y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)}$$
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/
$$y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)}$$
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/
$$y \log{\left(\frac{1}{y - 1} \right)}^{2} + 2 y \log{\left(2 \right)} \log{\left(\frac{1}{y - 1} \right)} + 2 y \log{\left(\frac{1}{y - 1} \right)} + y \log{\left(2 \right)}^{2} + 2 y \log{\left(2 \right)} + 2 y + 2 \log{\left(\frac{1}{y - 1} \right)} \log{\left(y - 1 \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(y - 1 \right)} + 2 \log{\left(y - 1 \right)}$$
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/
$$y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y \log{\left(\frac{2}{y - 1} \right)} + 2 y + 2 \log{\left(\frac{2}{y - 1} \right)} \log{\left(y - 1 \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)}$$
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/
$$y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)}$$
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/
$$y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)}$$
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/
$$y \log{\left(\frac{1}{y - 1} \right)}^{2} + 2 y \log{\left(2 \right)} \log{\left(\frac{1}{y - 1} \right)} + 2 y \log{\left(\frac{1}{y - 1} \right)} + y \log{\left(2 \right)}^{2} + 2 y \log{\left(2 \right)} + 2 y + 2 \log{\left(\frac{1}{y - 1} \right)} \log{\left(y - 1 \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(y - 1 \right)} + 2 \log{\left(y - 1 \right)}$$
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/
$$y \log{\left(\frac{2}{y - 1} \right)}^{2} + 2 y + 2 \left(y + \log{\left(y - 1 \right)}\right) \log{\left(\frac{2}{y - 1} \right)} + \log{\left(y - 1 \right)}^{2} + 2 \log{\left(y - 1 \right)}$$
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))