Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cos(x)*log((x^6+5)^(1/3))+2*x^5*sin(x)/(x^6+5)
¿Cómo vas a descomponer esta cos(x)*log((x^6+5)^(1/3))+2*x^5*sin(x)/(x^6+5) expresión en fracciones?
Solución
Ha introducido
[src]
/ ________\ 5
|3 / 6 | 2*x *sin(x)
cos(x)*log\\/ x + 5 / + -----------
6
x + 5
$$\frac{2 x^{5} \sin{\left(x \right)}}{x^{6} + 5} + \log{\left(\sqrt[3]{x^{6} + 5} \right)} \cos{\left(x \right)}$$
cos(x)*log((x^6 + 5)^(1/3)) + ((2*x^5)*sin(x))/(x^6 + 5)
Simplificación general
[src]
/ 6\ / 6\
5 \5 + x /*cos(x)*log\5 + x /
2*x *sin(x) + ---------------------------
3
-----------------------------------------
6
5 + x
$$\frac{2 x^{5} \sin{\left(x \right)} + \frac{\left(x^{6} + 5\right) \log{\left(x^{6} + 5 \right)} \cos{\left(x \right)}}{3}}{x^{6} + 5}$$
(2*x^5*sin(x) + (5 + x^6)*cos(x)*log(5 + x^6)/3)/(5 + x^6)
Respuesta numérica
[src]
cos(x)*log((x^6 + 5)^(1/3)) + 2.0*x^5*sin(x)/(5.0 + x^6)
cos(x)*log((x^6 + 5)^(1/3)) + 2.0*x^5*sin(x)/(5.0 + x^6)
Combinatoria
[src]
/ 6\ 5 6 / 6\
5*cos(x)*log\5 + x / + 6*x *sin(x) + x *cos(x)*log\5 + x /
----------------------------------------------------------
/ 6\
3*\5 + x /
$$\frac{x^{6} \log{\left(x^{6} + 5 \right)} \cos{\left(x \right)} + 6 x^{5} \sin{\left(x \right)} + 5 \log{\left(x^{6} + 5 \right)} \cos{\left(x \right)}}{3 \left(x^{6} + 5\right)}$$
(5*cos(x)*log(5 + x^6) + 6*x^5*sin(x) + x^6*cos(x)*log(5 + x^6))/(3*(5 + x^6))
Denominador racional
[src]
/ ________\ / ________\
5 |3 / 6 | 6 |3 / 6 |
2*x *sin(x) + 5*cos(x)*log\\/ 5 + x / + x *cos(x)*log\\/ 5 + x /
--------------------------------------------------------------------
6
5 + x
$$\frac{x^{6} \log{\left(\sqrt[3]{x^{6} + 5} \right)} \cos{\left(x \right)} + 2 x^{5} \sin{\left(x \right)} + 5 \log{\left(\sqrt[3]{x^{6} + 5} \right)} \cos{\left(x \right)}}{x^{6} + 5}$$
(2*x^5*sin(x) + 5*cos(x)*log((5 + x^6)^(1/3)) + x^6*cos(x)*log((5 + x^6)^(1/3)))/(5 + x^6)
Potencias
[src]
/ I*x -I*x\ / ________\ 5 / -I*x I*x\
|e e | |3 / 6 | I*x *\- e + e /
|---- + -----|*log\\/ 5 + x / - ---------------------
\ 2 2 / 6
5 + x
$$- \frac{i x^{5} \left(e^{i x} - e^{- i x}\right)}{x^{6} + 5} + \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \log{\left(\sqrt[3]{x^{6} + 5} \right)}$$
(exp(i*x)/2 + exp(-i*x)/2)*log((5 + x^6)^(1/3)) - i*x^5*(-exp(-i*x) + exp(i*x))/(5 + x^6)
Denominador común
[src]
/ 6\ 5
cos(x)*log\5 + x / 2*x *sin(x)
------------------ + -----------
3 6
5 + x
$$\frac{2 x^{5} \sin{\left(x \right)}}{x^{6} + 5} + \frac{\log{\left(x^{6} + 5 \right)} \cos{\left(x \right)}}{3}$$
cos(x)*log(5 + x^6)/3 + 2*x^5*sin(x)/(5 + x^6)
Parte trigonométrica
[src]
5 / pi\
/ ________\ 2*x *cos|x - --|
|3 / 6 | \ 2 /
cos(x)*log\\/ 5 + x / + ----------------
6
5 + x
$$\frac{2 x^{5} \cos{\left(x - \frac{\pi}{2} \right)}}{x^{6} + 5} + \log{\left(\sqrt[3]{x^{6} + 5} \right)} \cos{\left(x \right)}$$
/ ________\ 5
|3 / 6 | / pi\ 2*x *sin(x)
log\\/ 5 + x /*sin|x + --| + -----------
\ 2 / 6
5 + x
$$\frac{2 x^{5} \sin{\left(x \right)}}{x^{6} + 5} + \log{\left(\sqrt[3]{x^{6} + 5} \right)} \sin{\left(x + \frac{\pi}{2} \right)}$$
/ ________\
|3 / 6 | 5
log\\/ 5 + x / 2*x
---------------- + ---------------
sec(x) / 6\
\5 + x /*csc(x)
$$\frac{2 x^{5}}{\left(x^{6} + 5\right) \csc{\left(x \right)}} + \frac{\log{\left(\sqrt[3]{x^{6} + 5} \right)}}{\sec{\left(x \right)}}$$
/ ________\
/ 2/x\\ |3 / 6 | 5 /x\
|-1 + cot |-||*log\\/ 5 + x / 4*x *cot|-|
\ \2// \2/
------------------------------- + ----------------------
2/x\ / 2/x\\ / 6\
1 + cot |-| |1 + cot |-||*\5 + x /
\2/ \ \2//
$$\frac{4 x^{5} \cot{\left(\frac{x}{2} \right)}}{\left(x^{6} + 5\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \log{\left(\sqrt[3]{x^{6} + 5} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}$$
/ ________\
|3 / 6 | 5
log\\/ 5 + x / 2*x
---------------- + ---------------
/pi \ / 6\
csc|-- - x| \5 + x /*csc(x)
\2 /
$$\frac{2 x^{5}}{\left(x^{6} + 5\right) \csc{\left(x \right)}} + \frac{\log{\left(\sqrt[3]{x^{6} + 5} \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}$$
/ ________\
|3 / 6 | 5
log\\/ 5 + x / 2*x
---------------- + --------------------
sec(x) / 6\ / pi\
\5 + x /*sec|x - --|
\ 2 /
$$\frac{2 x^{5}}{\left(x^{6} + 5\right) \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{\log{\left(\sqrt[3]{x^{6} + 5} \right)}}{\sec{\left(x \right)}}$$
/ ________\
/ 2/x\\ |3 / 6 | 5 /x\
|1 - tan |-||*log\\/ 5 + x / 4*x *tan|-|
\ \2// \2/
------------------------------ + ----------------------
2/x\ / 2/x\\ / 6\
1 + tan |-| |1 + tan |-||*\5 + x /
\2/ \ \2//
$$\frac{4 x^{5} \tan{\left(\frac{x}{2} \right)}}{\left(x^{6} + 5\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \log{\left(\sqrt[3]{x^{6} + 5} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
(1 - tan(x/2)^2)*log((5 + x^6)^(1/3))/(1 + tan(x/2)^2) + 4*x^5*tan(x/2)/((1 + tan(x/2)^2)*(5 + x^6))
Unión de expresiones racionales
[src]
/ ________\
5 / 6\ |3 / 6 |
2*x *sin(x) + \5 + x /*cos(x)*log\\/ 5 + x /
----------------------------------------------
6
5 + x
$$\frac{2 x^{5} \sin{\left(x \right)} + \left(x^{6} + 5\right) \log{\left(\sqrt[3]{x^{6} + 5} \right)} \cos{\left(x \right)}}{x^{6} + 5}$$
(2*x^5*sin(x) + (5 + x^6)*cos(x)*log((5 + x^6)^(1/3)))/(5 + x^6)