Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(7^x/2)/(2*log(7))-1/(2*log(7)*tan(7^x/2))
¿Cómo vas a descomponer esta tan(7^x/2)/(2*log(7))-1/(2*log(7)*tan(7^x/2)) expresión en fracciones?
Solución
Ha introducido
[src]
/ x\
|7 |
tan|--|
\2 / 1
-------- - ----------------
2*log(7) / x\
|7 |
2*log(7)*tan|--|
\2 /
$$\frac{\tan{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)}} - \frac{1}{2 \log{\left(7 \right)} \tan{\left(\frac{7^{x}}{2} \right)}}$$
tan(7^x/2)/((2*log(7))) - 1/((2*log(7))*tan(7^x/2))
Simplificación general
[src]
/ x\
1 |7 |
- ------- + tan|--|
/ x\ \2 /
|7 |
tan|--|
\2 /
-------------------
2*log(7)
$$\frac{\tan{\left(\frac{7^{x}}{2} \right)} - \frac{1}{\tan{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}}$$
(-1/tan(7^x/2) + tan(7^x/2))/(2*log(7))
Respuesta numérica
[src]
0.256949171184875*tan(7^x/2) - 0.256949171184875/tan(7^x/2)
0.256949171184875*tan(7^x/2) - 0.256949171184875/tan(7^x/2)
Denominador racional
[src]
/ x\
2|7 |
-2*log(7) + 2*tan |--|*log(7)
\2 /
-----------------------------
/ x\
2 |7 |
4*log (7)*tan|--|
\2 /
$$\frac{2 \log{\left(7 \right)} \tan^{2}{\left(\frac{7^{x}}{2} \right)} - 2 \log{\left(7 \right)}}{4 \log{\left(7 \right)}^{2} \tan{\left(\frac{7^{x}}{2} \right)}}$$
(-2*log(7) + 2*tan(7^x/2)^2*log(7))/(4*log(7)^2*tan(7^x/2))
Denominador común
[src]
/ x\
2|7 |
-1 + tan |--|
\2 /
----------------
/ x\
|7 |
2*log(7)*tan|--|
\2 /
$$\frac{\tan^{2}{\left(\frac{7^{x}}{2} \right)} - 1}{2 \log{\left(7 \right)} \tan{\left(\frac{7^{x}}{2} \right)}}$$
(-1 + tan(7^x/2)^2)/(2*log(7)*tan(7^x/2))
Combinatoria
[src]
/ / x\\ / / x\\
| |7 || | |7 ||
|1 + tan|--||*|-1 + tan|--||
\ \2 // \ \2 //
----------------------------
/ x\
|7 |
2*log(7)*tan|--|
\2 /
$$\frac{\left(\tan{\left(\frac{7^{x}}{2} \right)} - 1\right) \left(\tan{\left(\frac{7^{x}}{2} \right)} + 1\right)}{2 \log{\left(7 \right)} \tan{\left(\frac{7^{x}}{2} \right)}}$$
(1 + tan(7^x/2))*(-1 + tan(7^x/2))/(2*log(7)*tan(7^x/2))
Potencias
[src]
/ x x \ / x x \
| I*7 -I*7 | | I*7 -I*7 |
| ---- ------| | ---- ------|
| 2 2 | | 2 2 |
I*\e + e / I*\- e + e /
---------------------------- + --------------------------
/ x x \ / x x \
| I*7 -I*7 | | I*7 -I*7 |
| ---- ------| | ---- ------|
| 2 2 | | 2 2 |
2*\- e + e /*log(7) 2*\e + e /*log(7)
$$\frac{i \left(- e^{\frac{7^{x} i}{2}} + e^{- \frac{7^{x} i}{2}}\right)}{2 \left(e^{\frac{7^{x} i}{2}} + e^{- \frac{7^{x} i}{2}}\right) \log{\left(7 \right)}} + \frac{i \left(e^{\frac{7^{x} i}{2}} + e^{- \frac{7^{x} i}{2}}\right)}{2 \left(- e^{\frac{7^{x} i}{2}} + e^{- \frac{7^{x} i}{2}}\right) \log{\left(7 \right)}}$$
i*(exp(i*7^x/2) + exp(-i*7^x/2))/(2*(-exp(i*7^x/2) + exp(-i*7^x/2))*log(7)) + i*(-exp(i*7^x/2) + exp(-i*7^x/2))/(2*(exp(i*7^x/2) + exp(-i*7^x/2))*log(7))
Parte trigonométrica
[src]
/ / x\\
| 2|7 ||
2/ x\ 2*|1 - tan |--||
1 - tan \7 / \ \2 //
-1 - ------------ + ----------------
2/ x\ / x\
1 + tan \7 / 2|7 |
1 + tan |--|
\2 /
--------------------------------------
/ / x\ \
| |7 | |
| 4*tan|--| / x\ |
| \2 / 2*tan\7 / |
|- ------------ + ------------|*log(7)
| / x\ 2/ x\|
| 2|7 | 1 + tan \7 /|
| 1 + tan |--| |
\ \2 / /
$$\frac{\frac{2 \left(1 - \tan^{2}{\left(\frac{7^{x}}{2} \right)}\right)}{\tan^{2}{\left(\frac{7^{x}}{2} \right)} + 1} - \frac{1 - \tan^{2}{\left(7^{x} \right)}}{\tan^{2}{\left(7^{x} \right)} + 1} - 1}{\left(\frac{2 \tan{\left(7^{x} \right)}}{\tan^{2}{\left(7^{x} \right)} + 1} - \frac{4 \tan{\left(\frac{7^{x}}{2} \right)}}{\tan^{2}{\left(\frac{7^{x}}{2} \right)} + 1}\right) \log{\left(7 \right)}}$$
/ x\
1 |7 |
------- - cot|--|
/ x\ \2 /
|7 |
cot|--|
\2 /
-----------------
2*log(7)
$$\frac{- \cot{\left(\frac{7^{x}}{2} \right)} + \frac{1}{\cot{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}}$$
/ x\ / x\
|7 | |7 |
sin|--| cos|--|
\2 / \2 /
---------------- - ----------------
/ x\ / x\
|7 | |7 |
2*cos|--|*log(7) 2*log(7)*sin|--|
\2 / \2 /
$$\frac{\sin{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \cos{\left(\frac{7^{x}}{2} \right)}} - \frac{\cos{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \sin{\left(\frac{7^{x}}{2} \right)}}$$
/ x \ / x\
|7 pi| |7 |
cos|-- - --| cos|--|
\2 2 / \2 /
---------------- - ---------------------
/ x\ / x \
|7 | |7 pi|
2*cos|--|*log(7) 2*cos|-- - --|*log(7)
\2 / \2 2 /
$$- \frac{\cos{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \cos{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}} + \frac{\cos{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}}{2 \log{\left(7 \right)} \cos{\left(\frac{7^{x}}{2} \right)}}$$
/ x\
|7 |
cot|--|
1 \2 /
---------------- - --------
/ x\ 2*log(7)
|7 |
2*cot|--|*log(7)
\2 /
$$- \frac{\cot{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)}} + \frac{1}{2 \log{\left(7 \right)} \cot{\left(\frac{7^{x}}{2} \right)}}$$
/ x\
2|7 |
2*sin |--| / x\
\2 / sin\7 /
---------- - ----------
/ x\ / x\
sin\7 / 2|7 |
2*sin |--|
\2 /
-----------------------
2*log(7)
$$\frac{\frac{2 \sin^{2}{\left(\frac{7^{x}}{2} \right)}}{\sin{\left(7^{x} \right)}} - \frac{\sin{\left(7^{x} \right)}}{2 \sin^{2}{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}}$$
/ x\ / x\
|7 | |7 |
sec|--| csc|--|
\2 / \2 /
---------------- - ----------------
/ x\ / x\
|7 | |7 |
2*csc|--|*log(7) 2*log(7)*sec|--|
\2 / \2 /
$$- \frac{\csc{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \sec{\left(\frac{7^{x}}{2} \right)}} + \frac{\sec{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \csc{\left(\frac{7^{x}}{2} \right)}}$$
/ / x\\ / x\
\1 - cos\7 //*cos\7 /
-----------------------------
/ / x\\ / x\
\-1 + cos\7 //*log(7)*sin\7 /
$$\frac{\left(1 - \cos{\left(7^{x} \right)}\right) \cos{\left(7^{x} \right)}}{\left(\cos{\left(7^{x} \right)} - 1\right) \log{\left(7 \right)} \sin{\left(7^{x} \right)}}$$
/ x\ / x\ -1 - cos\2*7 / + 2*cos\7 / -------------------------------- / / x\ / x\\ \- 2*sin\7 / + sin\2*7 //*log(7)
$$\frac{2 \cos{\left(7^{x} \right)} - \cos{\left(2 \cdot 7^{x} \right)} - 1}{\left(- 2 \sin{\left(7^{x} \right)} + \sin{\left(2 \cdot 7^{x} \right)}\right) \log{\left(7 \right)}}$$
/ x\
1 |7 |
- ------- + tan|--|
/ x\ \2 /
|7 |
tan|--|
\2 /
-------------------
2*log(7)
$$\frac{\tan{\left(\frac{7^{x}}{2} \right)} - \frac{1}{\tan{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}}$$
1 2
-1 - --------- + -------
/ x\ / x\
sec\2*7 / sec\7 /
--------------------------------------
/ 1 2 \
|-------------- - ------------|*log(7)
| / x pi\ / x pi\|
|sec|2*7 - --| sec|7 - --||
\ \ 2 / \ 2 //
$$\frac{-1 - \frac{1}{\sec{\left(2 \cdot 7^{x} \right)}} + \frac{2}{\sec{\left(7^{x} \right)}}}{\left(\frac{1}{\sec{\left(2 \cdot 7^{x} - \frac{\pi}{2} \right)}} - \frac{2}{\sec{\left(7^{x} - \frac{\pi}{2} \right)}}\right) \log{\left(7 \right)}}$$
/ x\ / x\
|pi 7 | |7 |
csc|-- - --| csc|--|
\2 2 / \2 /
------------ - ------------
/ x\ / x\
|7 | |pi 7 |
csc|--| csc|-- - --|
\2 / \2 2 /
---------------------------
2*log(7)
$$\frac{- \frac{\csc{\left(\frac{7^{x}}{2} \right)}}{\csc{\left(- \frac{7^{x}}{2} + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- \frac{7^{x}}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}}$$
/pi x\ / x pi\
-1 - sin|-- + 2*7 | + 2*sin|7 + --|
\2 / \ 2 /
------------------------------------
/ / x\ / x\\
\- 2*sin\7 / + sin\2*7 //*log(7)
$$\frac{2 \sin{\left(7^{x} + \frac{\pi}{2} \right)} - \sin{\left(2 \cdot 7^{x} + \frac{\pi}{2} \right)} - 1}{\left(- 2 \sin{\left(7^{x} \right)} + \sin{\left(2 \cdot 7^{x} \right)}\right) \log{\left(7 \right)}}$$
/ x\
2|7 |
/ x\ 2*sin |--|
sin\7 / \2 /
- ----------- + ----------
/ x\ / x\
1 - cos\7 / sin\7 /
--------------------------
2*log(7)
$$\frac{\frac{2 \sin^{2}{\left(\frac{7^{x}}{2} \right)}}{\sin{\left(7^{x} \right)}} - \frac{\sin{\left(7^{x} \right)}}{1 - \cos{\left(7^{x} \right)}}}{2 \log{\left(7 \right)}}$$
/ / x\\
| 2|7 ||
2/ x\ 2*|-1 + cot |--||
-1 + cot \7 / \ \2 //
-1 - ------------- + -----------------
2/ x\ / x\
1 + cot \7 / 2|7 |
1 + cot |--|
\2 /
--------------------------------------
/ / x\ \
| |7 | |
| 4*cot|--| / x\ |
| \2 / 2*cot\7 / |
|- ------------ + ------------|*log(7)
| / x\ 2/ x\|
| 2|7 | 1 + cot \7 /|
| 1 + cot |--| |
\ \2 / /
$$\frac{\frac{2 \left(\cot^{2}{\left(\frac{7^{x}}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{7^{x}}{2} \right)} + 1} - \frac{\cot^{2}{\left(7^{x} \right)} - 1}{\cot^{2}{\left(7^{x} \right)} + 1} - 1}{\left(\frac{2 \cot{\left(7^{x} \right)}}{\cot^{2}{\left(7^{x} \right)} + 1} - \frac{4 \cot{\left(\frac{7^{x}}{2} \right)}}{\cot^{2}{\left(\frac{7^{x}}{2} \right)} + 1}\right) \log{\left(7 \right)}}$$
1 2
-1 - -------------- + ------------
/pi x\ /pi x\
csc|-- - 2*7 | csc|-- - 7 |
\2 / \2 /
----------------------------------
/ 1 2 \
|--------- - -------|*log(7)
| / x\ / x\|
\csc\2*7 / csc\7 //
$$\frac{-1 + \frac{2}{\csc{\left(- 7^{x} + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(- 2 \cdot 7^{x} + \frac{\pi}{2} \right)}}}{\left(\frac{1}{\csc{\left(2 \cdot 7^{x} \right)}} - \frac{2}{\csc{\left(7^{x} \right)}}\right) \log{\left(7 \right)}}$$
/ x\ / x \
|7 | |7 pi|
sec|--| sec|-- - --|
\2 / \2 2 /
--------------------- - ----------------
/ x \ / x\
|7 pi| |7 |
2*log(7)*sec|-- - --| 2*log(7)*sec|--|
\2 2 / \2 /
$$\frac{\sec{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \sec{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}} - \frac{\sec{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}}{2 \log{\left(7 \right)} \sec{\left(\frac{7^{x}}{2} \right)}}$$
/ x\
2|7 |
sin |--| / x\
\2 / sin\7 /
-------------- - -----------------
/ x\ / x\
log(7)*sin\7 / 2|7 |
4*log(7)*sin |--|
\2 /
$$\frac{\sin^{2}{\left(\frac{7^{x}}{2} \right)}}{\log{\left(7 \right)} \sin{\left(7^{x} \right)}} - \frac{\sin{\left(7^{x} \right)}}{4 \log{\left(7 \right)} \sin^{2}{\left(\frac{7^{x}}{2} \right)}}$$
/ x\ / x \
|7 | |7 pi|
sec|--| sec|-- - --|
\2 / \2 2 /
------------ - ------------
/ x \ / x\
|7 pi| |7 |
sec|-- - --| sec|--|
\2 2 / \2 /
---------------------------
2*log(7)
$$\frac{\frac{\sec{\left(\frac{7^{x}}{2} \right)}}{\sec{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}} - \frac{\sec{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}}{\sec{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}}$$
/ x \ / x\
|7 pi| |7 |
cos|-- - --| cos|--|
\2 2 / \2 /
------------ - ------------
/ x\ / x \
|7 | |7 pi|
cos|--| cos|-- - --|
\2 / \2 2 /
---------------------------
2*log(7)
$$\frac{- \frac{\cos{\left(\frac{7^{x}}{2} \right)}}{\cos{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}} + \frac{\cos{\left(\frac{7^{x}}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{7^{x}}{2} \right)}}}{2 \log{\left(7 \right)}}$$
/ x\ / x\
|7 | |7 |
- cot|--| + tan|--|
\2 / \2 /
-------------------
2*log(7)
$$\frac{\tan{\left(\frac{7^{x}}{2} \right)} - \cot{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)}}$$
/ x\ / x\
-1 - cos\2*7 / + 2*cos\7 /
------------------------------------------
/ / x pi\ / x pi\\
|- 2*cos|7 - --| + cos|2*7 - --||*log(7)
\ \ 2 / \ 2 //
$$\frac{2 \cos{\left(7^{x} \right)} - \cos{\left(2 \cdot 7^{x} \right)} - 1}{\left(- 2 \cos{\left(7^{x} - \frac{\pi}{2} \right)} + \cos{\left(2 \cdot 7^{x} - \frac{\pi}{2} \right)}\right) \log{\left(7 \right)}}$$
/ x\ / x\
|pi 7 | |7 |
csc|-- - --| csc|--|
\2 2 / \2 /
---------------- - ---------------------
/ x\ / x\
|7 | |pi 7 |
2*csc|--|*log(7) 2*csc|-- - --|*log(7)
\2 / \2 2 /
$$- \frac{\csc{\left(\frac{7^{x}}{2} \right)}}{2 \log{\left(7 \right)} \csc{\left(- \frac{7^{x}}{2} + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- \frac{7^{x}}{2} + \frac{\pi}{2} \right)}}{2 \log{\left(7 \right)} \csc{\left(\frac{7^{x}}{2} \right)}}$$
csc(pi/2 - 7^x/2)/(2*csc(7^x/2)*log(7)) - csc(7^x/2)/(2*csc(pi/2 - 7^x/2)*log(7))
Unión de expresiones racionales
[src]
/ x\
2|7 |
-1 + tan |--|
\2 /
----------------
/ x\
|7 |
2*log(7)*tan|--|
\2 /
$$\frac{\tan^{2}{\left(\frac{7^{x}}{2} \right)} - 1}{2 \log{\left(7 \right)} \tan{\left(\frac{7^{x}}{2} \right)}}$$
(-1 + tan(7^x/2)^2)/(2*log(7)*tan(7^x/2))