Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan(x)^5/((x-3)*log(2))+5*atan(x)^4*log(x-3)/((1+x^2)*log(2))
¿Cómo vas a descomponer esta atan(x)^5/((x-3)*log(2))+5*atan(x)^4*log(x-3)/((1+x^2)*log(2)) expresión en fracciones?
Solución
Ha introducido
[src]
5 4
atan (x) 5*atan (x)*log(x - 3)
-------------- + ---------------------
(x - 3)*log(2) / 2\
\1 + x /*log(2)
$$\frac{\log{\left(x - 3 \right)} 5 \operatorname{atan}^{4}{\left(x \right)}}{\left(x^{2} + 1\right) \log{\left(2 \right)}} + \frac{\operatorname{atan}^{5}{\left(x \right)}}{\left(x - 3\right) \log{\left(2 \right)}}$$
atan(x)^5/(((x - 3)*log(2))) + ((5*atan(x)^4)*log(x - 3))/(((1 + x^2)*log(2)))
Simplificación general
[src]
4 // 2\ \
atan (x)*\\1 + x /*atan(x) + 5*(-3 + x)*log(-3 + x)/
----------------------------------------------------
/ 2\
\1 + x /*(-3 + x)*log(2)
$$\frac{\left(5 \left(x - 3\right) \log{\left(x - 3 \right)} + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{4}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right) \log{\left(2 \right)}}$$
atan(x)^4*((1 + x^2)*atan(x) + 5*(-3 + x)*log(-3 + x))/((1 + x^2)*(-3 + x)*log(2))
Respuesta numérica
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atan(x)^5/(-2.07944154167984 + 0.693147180559945*x) + 5.0*atan(x)^4*log(x - 3)/(0.693147180559945 + 0.693147180559945*x^2)
atan(x)^5/(-2.07944154167984 + 0.693147180559945*x) + 5.0*atan(x)^4*log(x - 3)/(0.693147180559945 + 0.693147180559945*x^2)
Denominador común
[src]
5 2 5 4 4
atan (x) + x *atan (x) - 15*atan (x)*log(-3 + x) + 5*x*atan (x)*log(-3 + x)
---------------------------------------------------------------------------
3 2
-3*log(2) + x*log(2) + x *log(2) - 3*x *log(2)
$$\frac{x^{2} \operatorname{atan}^{5}{\left(x \right)} + 5 x \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)} - 15 \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)} + \operatorname{atan}^{5}{\left(x \right)}}{x^{3} \log{\left(2 \right)} - 3 x^{2} \log{\left(2 \right)} + x \log{\left(2 \right)} - 3 \log{\left(2 \right)}}$$
(atan(x)^5 + x^2*atan(x)^5 - 15*atan(x)^4*log(-3 + x) + 5*x*atan(x)^4*log(-3 + x))/(-3*log(2) + x*log(2) + x^3*log(2) - 3*x^2*log(2))
Unión de expresiones racionales
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4 // 2\ \
atan (x)*\\1 + x /*atan(x) + 5*(-3 + x)*log(-3 + x)/
----------------------------------------------------
/ 2\
\1 + x /*(-3 + x)*log(2)
$$\frac{\left(5 \left(x - 3\right) \log{\left(x - 3 \right)} + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{4}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right) \log{\left(2 \right)}}$$
atan(x)^4*((1 + x^2)*atan(x) + 5*(-3 + x)*log(-3 + x))/((1 + x^2)*(-3 + x)*log(2))
Combinatoria
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4 / 2 \
atan (x)*\-15*log(-3 + x) + x *atan(x) + 5*x*log(-3 + x) + atan(x)/
-------------------------------------------------------------------
/ 2\
\1 + x /*(-3 + x)*log(2)
$$\frac{\left(x^{2} \operatorname{atan}{\left(x \right)} + 5 x \log{\left(x - 3 \right)} - 15 \log{\left(x - 3 \right)} + \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{4}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right) \log{\left(2 \right)}}$$
atan(x)^4*(-15*log(-3 + x) + x^2*atan(x) + 5*x*log(-3 + x) + atan(x))/((1 + x^2)*(-3 + x)*log(2))
Potencias
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5 4
atan (x) 5*atan (x)*log(-3 + x)
--------------- + ----------------------
(-3 + x)*log(2) / 2\
\1 + x /*log(2)
$$\frac{5 \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)}}{\left(x^{2} + 1\right) \log{\left(2 \right)}} + \frac{\operatorname{atan}^{5}{\left(x \right)}}{\left(x - 3\right) \log{\left(2 \right)}}$$
atan(x)^5/((-3 + x)*log(2)) + 5*atan(x)^4*log(-3 + x)/((1 + x^2)*log(2))
Parte trigonométrica
[src]
5 4
atan (x) 5*atan (x)*log(-3 + x)
--------------- + ----------------------
(-3 + x)*log(2) / 2\
\1 + x /*log(2)
$$\frac{5 \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)}}{\left(x^{2} + 1\right) \log{\left(2 \right)}} + \frac{\operatorname{atan}^{5}{\left(x \right)}}{\left(x - 3\right) \log{\left(2 \right)}}$$
atan(x)^5/((-3 + x)*log(2)) + 5*atan(x)^4*log(-3 + x)/((1 + x^2)*log(2))
Denominador racional
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5 2 5 4 4
atan (x)*log(2) + x *atan (x)*log(2) - 15*atan (x)*log(2)*log(-3 + x) + 5*x*atan (x)*log(2)*log(-3 + x)
-------------------------------------------------------------------------------------------------------
/ 2\ 2
\1 + x /*(-3 + x)*log (2)
$$\frac{x^{2} \log{\left(2 \right)} \operatorname{atan}^{5}{\left(x \right)} + 5 x \log{\left(2 \right)} \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)} - 15 \log{\left(2 \right)} \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)} + \log{\left(2 \right)} \operatorname{atan}^{5}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right) \log{\left(2 \right)}^{2}}$$
(atan(x)^5*log(2) + x^2*atan(x)^5*log(2) - 15*atan(x)^4*log(2)*log(-3 + x) + 5*x*atan(x)^4*log(2)*log(-3 + x))/((1 + x^2)*(-3 + x)*log(2)^2)
Compilar la expresión
[src]
5 4
atan (x) 5*atan (x)*log(x - 3)
--------------- + ---------------------
(-3 + x)*log(2) / 2\
\1 + x /*log(2)
$$\frac{5 \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)}}{\left(x^{2} + 1\right) \log{\left(2 \right)}} + \frac{\operatorname{atan}^{5}{\left(x \right)}}{\left(x - 3\right) \log{\left(2 \right)}}$$
atan(x)^5/((-3 + x)*log(2)) + 5*atan(x)^4*log(x - 3)/((1 + x^2)*log(2))