Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2+1)/2-log(x+1)+atan(x)-1/(1+x)
¿Cómo vas a descomponer esta log(x^2+1)/2-log(x+1)+atan(x)-1/(1+x) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2 \
log\x + 1/ 1
----------- - log(x + 1) + atan(x) - -----
2 1 + x
$$\left(\left(- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2}\right) + \operatorname{atan}{\left(x \right)}\right) - \frac{1}{x + 1}$$
log(x^2 + 1)/2 - log(x + 1) + atan(x) - 1/(1 + x)
Simplificación general
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/ / 2\\
-2 + (1 + x)*\-2*log(1 + x) + 2*atan(x) + log\1 + x //
------------------------------------------------------
2*(1 + x)
$$\frac{\left(x + 1\right) \left(- 2 \log{\left(x + 1 \right)} + \log{\left(x^{2} + 1 \right)} + 2 \operatorname{atan}{\left(x \right)}\right) - 2}{2 \left(x + 1\right)}$$
(-2 + (1 + x)*(-2*log(1 + x) + 2*atan(x) + log(1 + x^2)))/(2*(1 + x))
Parte trigonométrica
[src]
/ 2\
log\1 + x / 1
----------- - ----- - log(1 + x) + atan(x)
2 1 + x
$$- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)} - \frac{1}{x + 1}$$
log(1 + x^2)/2 - 1/(1 + x) - log(1 + x) + atan(x)
Denominador común
[src]
/ 2\
log\1 + x / 1
----------- - ----- - log(1 + x) + atan(x)
2 1 + x
$$- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)} - \frac{1}{x + 1}$$
log(1 + x^2)/2 - 1/(1 + x) - log(1 + x) + atan(x)
Respuesta numérica
[src]
-1/(1.0 + x) - log(x + 1) + 0.5*log(x^2 + 1) + atan(x)
-1/(1.0 + x) - log(x + 1) + 0.5*log(x^2 + 1) + atan(x)
Unión de expresiones racionales
[src]
/ / 2\\
-2 + (1 + x)*\-2*log(1 + x) + 2*atan(x) + log\1 + x //
------------------------------------------------------
2*(1 + x)
$$\frac{\left(x + 1\right) \left(- 2 \log{\left(x + 1 \right)} + \log{\left(x^{2} + 1 \right)} + 2 \operatorname{atan}{\left(x \right)}\right) - 2}{2 \left(x + 1\right)}$$
(-2 + (1 + x)*(-2*log(1 + x) + 2*atan(x) + log(1 + x^2)))/(2*(1 + x))
Combinatoria
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/ 2\ / 2\
-2 - 2*log(1 + x) + 2*atan(x) + x*log\1 + x / - 2*x*log(1 + x) + 2*x*atan(x) + log\1 + x /
------------------------------------------------------------------------------------------
2*(1 + x)
$$\frac{- 2 x \log{\left(x + 1 \right)} + x \log{\left(x^{2} + 1 \right)} + 2 x \operatorname{atan}{\left(x \right)} - 2 \log{\left(x + 1 \right)} + \log{\left(x^{2} + 1 \right)} + 2 \operatorname{atan}{\left(x \right)} - 2}{2 \left(x + 1\right)}$$
(-2 - 2*log(1 + x) + 2*atan(x) + x*log(1 + x^2) - 2*x*log(1 + x) + 2*x*atan(x) + log(1 + x^2))/(2*(1 + x))
Potencias
[src]
/ 2\
log\1 + x / 1
----------- - ----- - log(1 + x) + atan(x)
2 1 + x
$$- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)} - \frac{1}{x + 1}$$
log(1 + x^2)/2 - 1/(1 + x) - log(1 + x) + atan(x)
Denominador racional
[src]
/ 2\ / 2\
-2 - 2*log(1 + x) + 2*atan(x) + x*log\1 + x / - 2*x*log(1 + x) + 2*x*atan(x) + log\1 + x /
------------------------------------------------------------------------------------------
2 + 2*x
$$\frac{- 2 x \log{\left(x + 1 \right)} + x \log{\left(x^{2} + 1 \right)} + 2 x \operatorname{atan}{\left(x \right)} - 2 \log{\left(x + 1 \right)} + \log{\left(x^{2} + 1 \right)} + 2 \operatorname{atan}{\left(x \right)} - 2}{2 x + 2}$$
(-2 - 2*log(1 + x) + 2*atan(x) + x*log(1 + x^2) - 2*x*log(1 + x) + 2*x*atan(x) + log(1 + x^2))/(2 + 2*x)
Compilar la expresión
[src]
/ 2 \
log\x + 1/ 1
----------- - ----- - log(x + 1) + atan(x)
2 1 + x
$$- \log{\left(x + 1 \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \operatorname{atan}{\left(x \right)} - \frac{1}{x + 1}$$
log(x^2 + 1)/2 - 1/(1 + x) - log(x + 1) + atan(x)