Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
exp(x+2)/(x+sin(x)^(-1))^(1/3)+(cos(x)+tan(x))/(2*(log(x)/log(2)))
¿Cómo vas a descomponer esta exp(x+2)/(x+sin(x)^(-1))^(1/3)+(cos(x)+tan(x))/(2*(log(x)/log(2))) expresión en fracciones?
Solución
Ha introducido
[src]
x + 2
e cos(x) + tan(x)
---------------- + ---------------
____________ log(x)
/ 1 2*------
3 / x + ------ log(2)
\/ sin(x)
$$\frac{e^{x + 2}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}} + \frac{\cos{\left(x \right)} + \tan{\left(x \right)}}{2 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}}$$
exp(x + 2)/(x + 1/sin(x))^(1/3) + (cos(x) + tan(x))/((2*(log(x)/log(2))))
Simplificación general
[src]
2 + x
2*e *log(x)
cos(x)*log(2) + log(2)*tan(x) + ----------------
____________
/ 1
3 / x + ------
\/ sin(x)
------------------------------------------------
2*log(x)
$$\frac{\log{\left(2 \right)} \cos{\left(x \right)} + \log{\left(2 \right)} \tan{\left(x \right)} + \frac{2 e^{x + 2} \log{\left(x \right)}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}}{2 \log{\left(x \right)}}$$
(cos(x)*log(2) + log(2)*tan(x) + 2*exp(2 + x)*log(x)/(x + 1/sin(x))^(1/3))/(2*log(x))
Combinatoria
[src]
____________ ____________
/ 1 / 1 2 x
3 / x + ------ *cos(x)*log(2) + 3 / x + ------ *log(2)*tan(x) + 2*e *e *log(x)
\/ sin(x) \/ sin(x)
--------------------------------------------------------------------------------
____________
/ 1
2*3 / x + ------ *log(x)
\/ sin(x)
$$\frac{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(2 \right)} \cos{\left(x \right)} + \sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(2 \right)} \tan{\left(x \right)} + 2 e^{2} e^{x} \log{\left(x \right)}}{2 \sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(x \right)}}$$
((x + 1/sin(x))^(1/3)*cos(x)*log(2) + (x + 1/sin(x))^(1/3)*log(2)*tan(x) + 2*exp(2)*exp(x)*log(x))/(2*(x + 1/sin(x))^(1/3)*log(x))
Respuesta numérica
[src]
(x + 1/sin(x))^(-0.333333333333333)*exp(x + 2) + 0.346573590279973*(cos(x) + tan(x))/log(x)
(x + 1/sin(x))^(-0.333333333333333)*exp(x + 2) + 0.346573590279973*(cos(x) + tan(x))/log(x)
Unión de expresiones racionales
[src]
______________
2 + x / 1 + x*sin(x)
2*e *log(x) + 3 / ------------ *(cos(x) + tan(x))*log(2)
\/ sin(x)
-------------------------------------------------------------
______________
/ 1 + x*sin(x)
2*3 / ------------ *log(x)
\/ sin(x)
$$\frac{\sqrt[3]{\frac{x \sin{\left(x \right)} + 1}{\sin{\left(x \right)}}} \left(\cos{\left(x \right)} + \tan{\left(x \right)}\right) \log{\left(2 \right)} + 2 e^{x + 2} \log{\left(x \right)}}{2 \sqrt[3]{\frac{x \sin{\left(x \right)} + 1}{\sin{\left(x \right)}}} \log{\left(x \right)}}$$
(2*exp(2 + x)*log(x) + ((1 + x*sin(x))/sin(x))^(1/3)*(cos(x) + tan(x))*log(2))/(2*((1 + x*sin(x))/sin(x))^(1/3)*log(x))
Denominador común
[src]
____________ ____________
/ 1 / 1 2 x
3 / x + ------ *cos(x)*log(2) + 3 / x + ------ *log(2)*tan(x) + 2*e *e *log(x)
\/ sin(x) \/ sin(x)
--------------------------------------------------------------------------------
____________
/ 1
2*3 / x + ------ *log(x)
\/ sin(x)
$$\frac{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(2 \right)} \cos{\left(x \right)} + \sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(2 \right)} \tan{\left(x \right)} + 2 e^{2} e^{x} \log{\left(x \right)}}{2 \sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(x \right)}}$$
((x + 1/sin(x))^(1/3)*cos(x)*log(2) + (x + 1/sin(x))^(1/3)*log(2)*tan(x) + 2*exp(2)*exp(x)*log(x))/(2*(x + 1/sin(x))^(1/3)*log(x))
Denominador racional
[src]
____________ ____________
2 + x / 1 / 1
2*e *log(x) + 3 / x + ------ *cos(x)*log(2) + 3 / x + ------ *log(2)*tan(x)
\/ sin(x) \/ sin(x)
---------------------------------------------------------------------------------
____________
/ 1
2*3 / x + ------ *log(x)
\/ sin(x)
$$\frac{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(2 \right)} \cos{\left(x \right)} + \sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(2 \right)} \tan{\left(x \right)} + 2 e^{x + 2} \log{\left(x \right)}}{2 \sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}} \log{\left(x \right)}}$$
(2*exp(2 + x)*log(x) + (x + 1/sin(x))^(1/3)*cos(x)*log(2) + (x + 1/sin(x))^(1/3)*log(2)*tan(x))/(2*(x + 1/sin(x))^(1/3)*log(x))
Compilar la expresión
[src]
x + 2
e (cos(x) + tan(x))*log(2)
---------------- + ------------------------
____________ 2*log(x)
/ 1
3 / x + ------
\/ sin(x)
$$\frac{\left(\cos{\left(x \right)} + \tan{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}$$
exp(x + 2)/(x + 1/sin(x))^(1/3) + (cos(x) + tan(x))*log(2)/(2*log(x))
Parte trigonométrica
[src]
cosh(2 + x) + sinh(2 + x) (cos(x) + tan(x))*log(2)
------------------------- + ------------------------
3 ____________ 2*log(x)
\/ x + csc(x)
$$\frac{\left(\cos{\left(x \right)} + \tan{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \csc{\left(x \right)}}}$$
cosh(2 + x) + sinh(2 + x) (cos(x) + tan(x))*log(2)
------------------------- + ------------------------
____________ 2*log(x)
/ 1
3 / x + ------
\/ sin(x)
$$\frac{\left(\cos{\left(x \right)} + \tan{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}$$
/ 2/x\\
| -1 + cot |-||
| 1 \2/|
|------ + ------------|*log(2)
|cot(x) 2/x\ |
2 + x | 1 + cot |-| |
e \ \2/ /
------------------------- + ------------------------------
_________________ 2*log(x)
/ 2/x\
/ 1 + cot |-|
/ \2/
/ x + -----------
/ /x\
3 / 2*cot|-|
\/ \2/
$$\frac{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{1}{\cot{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{2 \cot{\left(\frac{x}{2} \right)}}}}$$
/ / pi\ \
|cos|x - --| |
| \ 2 / |
|----------- + cos(x)|*log(2)
cosh(2 + x) + sinh(2 + x) \ cos(x) /
------------------------- + -----------------------------
_________________ 2*log(x)
/ 1
/ x + -----------
/ / pi\
3 / cos|x - --|
\/ \ 2 /
$$\frac{\left(\cos{\left(x \right)} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \frac{1}{\cos{\left(x - \frac{\pi}{2} \right)}}}}$$
2 + x
e (cos(x) + tan(x))*log(2)
-------------- + ------------------------
3 ____________ 2*log(x)
\/ x + csc(x)
$$\frac{\left(\cos{\left(x \right)} + \tan{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \csc{\left(x \right)}}}$$
/ /pi \\
| csc|-- - x||
| 1 \2 /|
|----------- + -----------|*log(2)
| /pi \ csc(x) |
2 + x |csc|-- - x| |
e \ \2 / /
-------------- + ----------------------------------
3 ____________ 2*log(x)
\/ x + csc(x)
$$\frac{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \csc{\left(x \right)}}}$$
2 + x
e (cos(x) + tan(x))*log(2)
---------------- + ------------------------
____________ 2*log(x)
/ 1
3 / x + ------
\/ sin(x)
$$\frac{\left(\cos{\left(x \right)} + \tan{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}$$
/ 2/x\ \
|1 - tan |-| |
| \2/ |
|----------- + tan(x)|*log(2)
| 2/x\ |
|1 + tan |-| |
cosh(2 + x) + sinh(2 + x) \ \2/ /
------------------------- + -----------------------------
_________________ 2*log(x)
/ 2/x\
/ 1 + tan |-|
/ \2/
/ x + -----------
/ /x\
3 / 2*tan|-|
\/ \2/
$$\frac{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \tan{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{2 \tan{\left(\frac{x}{2} \right)}}}}$$
x + 2
e log(2)
---------------- + --------*(cos(x) + tan(x))
____________ 2*log(x)
/ 1
3 / x + ------
\/ sin(x)
$$\frac{\log{\left(2 \right)}}{2 \log{\left(x \right)}} \left(\cos{\left(x \right)} + \tan{\left(x \right)}\right) + \frac{e^{x + 2}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}$$
/ 2 \
|2*sin (x) / pi\|
|--------- + sin|x + --||*log(2)
cosh(2 + x) + sinh(2 + x) \ sin(2*x) \ 2 //
------------------------- + --------------------------------
____________ 2*log(x)
/ 1
3 / x + ------
\/ sin(x)
$$\frac{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + \sin{\left(x + \frac{\pi}{2} \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}$$
/ 1 sec(x) \
|------ + -----------|*log(2)
|sec(x) / pi\|
2 + x | sec|x - --||
e \ \ 2 //
--------------------- + -----------------------------
_________________ 2*log(x)
/ /pi \
3 / x + sec|-- - x|
\/ \2 /
$$\frac{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \sec{\left(- x + \frac{\pi}{2} \right)}}}$$
/ 1 sec(x) \
|------ + -----------|*log(2)
|sec(x) / pi\|
| sec|x - --||
cosh(2 + x) + sinh(2 + x) \ \ 2 //
------------------------- + -----------------------------
_________________ 2*log(x)
/ / pi\
3 / x + sec|x - --|
\/ \ 2 /
$$\frac{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \sec{\left(x - \frac{\pi}{2} \right)}}}$$
/ 2/x\ \
|1 - tan |-| |
| \2/ |
|----------- + tan(x)|*log(2)
| 2/x\ |
2 + x |1 + tan |-| |
e \ \2/ /
------------------------- + -----------------------------
_________________ 2*log(x)
/ 2/x\
/ 1 + tan |-|
/ \2/
/ x + -----------
/ /x\
3 / 2*tan|-|
\/ \2/
$$\frac{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \tan{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{2 \tan{\left(\frac{x}{2} \right)}}}}$$
/ 1 sec(x) \
|------ + -----------|*log(2)
|sec(x) / pi\|
2 + x | sec|x - --||
e \ \ 2 //
--------------------- + -----------------------------
_________________ 2*log(x)
/ / pi\
3 / x + sec|x - --|
\/ \ 2 /
$$\frac{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \sec{\left(x - \frac{\pi}{2} \right)}}}$$
/sin(x) \
|------ + cos(x)|*log(2)
cosh(2 + x) + sinh(2 + x) \cos(x) /
------------------------- + ------------------------
____________ 2*log(x)
/ 1
3 / x + ------
\/ sin(x)
$$\frac{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \cos{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}$$
/ /pi \\
| csc|-- - x||
| 1 \2 /|
|----------- + -----------|*log(2)
| /pi \ csc(x) |
|csc|-- - x| |
cosh(2 + x) + sinh(2 + x) \ \2 / /
------------------------- + ----------------------------------
3 ____________ 2*log(x)
\/ x + csc(x)
$$\frac{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \csc{\left(x \right)}}}$$
/ 1 sec(x)\
2 + x |------ + ------|*log(2)
e \sec(x) csc(x)/
-------------- + ------------------------
3 ____________ 2*log(x)
\/ x + csc(x)
$$\frac{\left(\frac{1}{\sec{\left(x \right)}} + \frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \csc{\left(x \right)}}}$$
/ 2/x\\
| -1 + cot |-||
| 1 \2/|
|------ + ------------|*log(2)
|cot(x) 2/x\ |
| 1 + cot |-| |
cosh(2 + x) + sinh(2 + x) \ \2/ /
------------------------- + ------------------------------
_________________ 2*log(x)
/ 2/x\
/ 1 + cot |-|
/ \2/
/ x + -----------
/ /x\
3 / 2*cot|-|
\/ \2/
$$\frac{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{1}{\cot{\left(x \right)}}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{2 \cot{\left(\frac{x}{2} \right)}}}}$$
/ 2 \
|2*sin (x) |
|--------- + cos(x)|*log(2)
cosh(2 + x) + sinh(2 + x) \ sin(2*x) /
------------------------- + ---------------------------
____________ 2*log(x)
/ 1
3 / x + ------
\/ sin(x)
$$\frac{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + \cos{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{\sinh{\left(x + 2 \right)} + \cosh{\left(x + 2 \right)}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}$$
(cosh(2 + x) + sinh(2 + x))/(x + 1/sin(x))^(1/3) + (2*sin(x)^2/sin(2*x) + cos(x))*log(2)/(2*log(x))
Potencias
[src]
2 + x
e (cos(x) + tan(x))*log(2)
---------------- + ------------------------
____________ 2*log(x)
/ 1
3 / x + ------
\/ sin(x)
$$\frac{\left(\cos{\left(x \right)} + \tan{\left(x \right)}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \frac{1}{\sin{\left(x \right)}}}}$$
/ I*x -I*x / I*x -I*x\\
|e e I*\- e + e /|
|---- + ----- + ------------------|*log(2)
2 + x | 2 2 I*x -I*x |
e \ e + e /
------------------------- + ------------------------------------------
____________________ 2*log(x)
/ 2*I
/ x + --------------
3 / -I*x I*x
\/ - e + e
$$\frac{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} + \frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \log{\left(2 \right)}}{2 \log{\left(x \right)}} + \frac{e^{x + 2}}{\sqrt[3]{x + \frac{2 i}{e^{i x} - e^{- i x}}}}$$
exp(2 + x)/(x + 2*i/(-exp(-i*x) + exp(i*x)))^(1/3) + (exp(i*x)/2 + exp(-i*x)/2 + i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))*log(2)/(2*log(x))