Sr Examen
¿Cómo vas a descomponer esta ln((x+(sqrt(x^2+1)))/(2x)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ________\ | / 2 | |x + \/ x + 1 | log|---------------| \ 2*x /
$$\log{\left(\frac{x + \sqrt{x^{2} + 1}}{2 x} \right)}$$
log((x + sqrt(x^2 + 1))/((2*x)))
Descomposición de una fracción
[src]
log(1/2 + sqrt(x^2 + 1)/(2*x))
$$\log{\left(\frac{1}{2} + \frac{\sqrt{x^{2} + 1}}{2 x} \right)}$$
/ ________\ | / 2 | |1 \/ x + 1 | log|- + -----------| \2 2*x /
Denominador común
[src]
/ ________\
| / 2 |
| \/ 1 + x |
-log(2) + log|1 + -----------|
\ x /
$$\log{\left(1 + \frac{\sqrt{x^{2} + 1}}{x} \right)} - \log{\left(2 \right)}$$
-log(2) + log(1 + sqrt(1 + x^2)/x)
Potencias
[src]
/ ________\ | / 2 | |x \/ 1 + x | |- + -----------| |2 2 | log|---------------| \ x /
$$\log{\left(\frac{\frac{x}{2} + \frac{\sqrt{x^{2} + 1}}{2}}{x} \right)}$$
log((x/2 + sqrt(1 + x^2)/2)/x)
Combinatoria
[src]
/ ________\
| / 2 |
| \/ 1 + x |
-log(2) + log|1 + -----------|
\ x /
$$\log{\left(1 + \frac{\sqrt{x^{2} + 1}}{x} \right)} - \log{\left(2 \right)}$$
-log(2) + log(1 + sqrt(1 + x^2)/x)