Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(((14*sin(x))/(1+cos(x))-2*sqrt(35))/(2*sqrt(35)+(14*sin(x))/(1+cos(x))))/sqrt(35)
¿Cómo vas a descomponer esta log(((14*sin(x))/(1+cos(x))-2*sqrt(35))/(2*sqrt(35)+(14*sin(x))/(1+cos(x))))/sqrt(35) expresión en fracciones?
Solución
Ha introducido
[src]
/14*sin(x) ____\
|---------- - 2*\/ 35 |
|1 + cos(x) |
log|---------------------|
| ____ 14*sin(x) |
|2*\/ 35 + ----------|
\ 1 + cos(x)/
--------------------------
____
\/ 35
$$\frac{\log{\left(\frac{- 2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{\sqrt{35}}$$
log(((14*sin(x))/(1 + cos(x)) - 2*sqrt(35))/(2*sqrt(35) + (14*sin(x))/(1 + cos(x))))/sqrt(35)
Descomposición de una fracción
[src]
sqrt(35)*log(-2*sqrt(35)/(2*sqrt(35) + (14*sin(x))/(1 + cos(x))) + 14*sin(x)/(2*sqrt(35) + (14*sin(x))/(1 + cos(x)) + 2*sqrt(35)*cos(x) + 14*cos(x)*sin(x)/(1 + cos(x))))/35
$$\frac{\sqrt{35} \log{\left(\frac{14 \sin{\left(x \right)}}{2 \sqrt{35} \cos{\left(x \right)} + 2 \sqrt{35} + \frac{14 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} - \frac{2 \sqrt{35}}{2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{35}$$
/ ____ \
____ | 2*\/ 35 14*sin(x) |
\/ 35 *log|- --------------------- + ----------------------------------------------------------|
| ____ 14*sin(x) ____ 14*sin(x) ____ 14*cos(x)*sin(x)|
| 2*\/ 35 + ---------- 2*\/ 35 + ---------- + 2*\/ 35 *cos(x) + ----------------|
\ 1 + cos(x) 1 + cos(x) 1 + cos(x) /
------------------------------------------------------------------------------------------------
35
Simplificación general
[src]
/ ____ \
____ |7*sin(x) - \/ 35 *(1 + cos(x))|
\/ 35 *log|------------------------------|
| ____ |
\7*sin(x) + \/ 35 *(1 + cos(x))/
------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- \sqrt{35} \left(\cos{\left(x \right)} + 1\right) + 7 \sin{\left(x \right)}}{\sqrt{35} \left(\cos{\left(x \right)} + 1\right) + 7 \sin{\left(x \right)}} \right)}}{35}$$
sqrt(35)*log((7*sin(x) - sqrt(35)*(1 + cos(x)))/(7*sin(x) + sqrt(35)*(1 + cos(x))))/35
Respuesta numérica
[src]
0.169030850945703*log(((14*sin(x))/(1 + cos(x)) - 2*sqrt(35))/(2*sqrt(35) + (14*sin(x))/(1 + cos(x))))
0.169030850945703*log(((14*sin(x))/(1 + cos(x)) - 2*sqrt(35))/(2*sqrt(35) + (14*sin(x))/(1 + cos(x))))
Denominador común
[src]
/ ____ \
____ | \/ 35 7*sin(x) |
\/ 35 *log|- ------------------- + -----------------------------------------------------|
| ____ 7*sin(x) ____ ____ 7*sin(x) 7*cos(x)*sin(x)|
| \/ 35 + ---------- \/ 35 + \/ 35 *cos(x) + ---------- + ---------------|
\ 1 + cos(x) 1 + cos(x) 1 + cos(x) /
-----------------------------------------------------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{7 \sin{\left(x \right)}}{\sqrt{35} \cos{\left(x \right)} + \sqrt{35} + \frac{7 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} - \frac{\sqrt{35}}{\sqrt{35} + \frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{35}$$
sqrt(35)*log(-sqrt(35)/(sqrt(35) + 7*sin(x)/(1 + cos(x))) + 7*sin(x)/(sqrt(35) + sqrt(35)*cos(x) + 7*sin(x)/(1 + cos(x)) + 7*cos(x)*sin(x)/(1 + cos(x))))/35
Unión de expresiones racionales
[src]
/ ____ \
____ |7*sin(x) - \/ 35 *(1 + cos(x))|
\/ 35 *log|------------------------------|
| ____ |
\7*sin(x) + \/ 35 *(1 + cos(x))/
------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- \sqrt{35} \left(\cos{\left(x \right)} + 1\right) + 7 \sin{\left(x \right)}}{\sqrt{35} \left(\cos{\left(x \right)} + 1\right) + 7 \sin{\left(x \right)}} \right)}}{35}$$
sqrt(35)*log((7*sin(x) - sqrt(35)*(1 + cos(x)))/(7*sin(x) + sqrt(35)*(1 + cos(x))))/35
Denominador racional
[src]
/ / / 2 2 \ / 2 \ / 2 2 \ / 2 \ \ \
| | / 2 2\ | 7*sin (x) 7*sin (x)*cos(x)| 2 | 7*sin (x) | | 7*sin (x) 7*sin (x)*cos(x)| ____ | 7*sin (x) | / 2 2\ | |
|-|5*\- 7*sin (x) + 5*(1 + cos(x)) /*|5 + 5*cos(x) - ------------- - ----------------| + 7*sin (x)*|5 - -------------|*|5 + 5*cos(x) - ------------- - ----------------| - 2*\/ 35 *|5 - -------------|*\- 7*sin (x) + 5*(1 + cos(x)) /*sin(x)| |
| | | 2 2 | | 2| | 2 2 | | 2| | |
____ | \ \ (1 + cos(x)) (1 + cos(x)) / \ (1 + cos(x)) / \ (1 + cos(x)) (1 + cos(x)) / \ (1 + cos(x)) / / |
\/ 35 *log|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| / 2 \ / 2 2 \ |
| | 7*sin (x) | / 2 2\ | 7*sin (x) 7*sin (x)*cos(x)| |
| |5 - -------------|*\- 7*sin (x) + 5*(1 + cos(x)) /*|5 + 5*cos(x) - ------------- - ----------------| |
| | 2| | 2 2 | |
\ \ (1 + cos(x)) / \ (1 + cos(x)) (1 + cos(x)) / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(- \frac{- 2 \sqrt{35} \left(5 - \frac{7 \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}}\right) \left(5 \left(\cos{\left(x \right)} + 1\right)^{2} - 7 \sin^{2}{\left(x \right)}\right) \sin{\left(x \right)} + 7 \left(5 - \frac{7 \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}}\right) \left(5 \cos{\left(x \right)} + 5 - \frac{7 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} - \frac{7 \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}}\right) \sin^{2}{\left(x \right)} + 5 \left(5 \left(\cos{\left(x \right)} + 1\right)^{2} - 7 \sin^{2}{\left(x \right)}\right) \left(5 \cos{\left(x \right)} + 5 - \frac{7 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} - \frac{7 \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}}\right)}{\left(5 - \frac{7 \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}}\right) \left(5 \left(\cos{\left(x \right)} + 1\right)^{2} - 7 \sin^{2}{\left(x \right)}\right) \left(5 \cos{\left(x \right)} + 5 - \frac{7 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} - \frac{7 \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}}\right)} \right)}}{35}$$
sqrt(35)*log(-(5*(-7*sin(x)^2 + 5*(1 + cos(x))^2)*(5 + 5*cos(x) - 7*sin(x)^2/(1 + cos(x))^2 - 7*sin(x)^2*cos(x)/(1 + cos(x))^2) + 7*sin(x)^2*(5 - 7*sin(x)^2/(1 + cos(x))^2)*(5 + 5*cos(x) - 7*sin(x)^2/(1 + cos(x))^2 - 7*sin(x)^2*cos(x)/(1 + cos(x))^2) - 2*sqrt(35)*(5 - 7*sin(x)^2/(1 + cos(x))^2)*(-7*sin(x)^2 + 5*(1 + cos(x))^2)*sin(x))/((5 - 7*sin(x)^2/(1 + cos(x))^2)*(-7*sin(x)^2 + 5*(1 + cos(x))^2)*(5 + 5*cos(x) - 7*sin(x)^2/(1 + cos(x))^2 - 7*sin(x)^2*cos(x)/(1 + cos(x))^2)))/35
Potencias
[src]
/ / -I*x I*x\\
| ____ 7*I*\- e + e /|
|- 2*\/ 35 - --------------------|
| I*x -I*x |
| e e |
| 1 + ---- + ----- |
____ | 2 2 |
\/ 35 *log|---------------------------------|
| / -I*x I*x\ |
| ____ 7*I*\- e + e / |
| 2*\/ 35 - -------------------- |
| I*x -I*x |
| e e |
| 1 + ---- + ----- |
\ 2 2 /
---------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- \frac{7 i \left(e^{i x} - e^{- i x}\right)}{\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}} - 2 \sqrt{35}}{- \frac{7 i \left(e^{i x} - e^{- i x}\right)}{\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}} + 2 \sqrt{35}} \right)}}{35}$$
/ ____ 14*sin(x) \
|- 2*\/ 35 + ----------|
____ | 1 + cos(x)|
\/ 35 *log|-----------------------|
| ____ 14*sin(x) |
| 2*\/ 35 + ---------- |
\ 1 + cos(x) /
-----------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{35}$$
sqrt(35)*log((-2*sqrt(35) + 14*sin(x)/(1 + cos(x)))/(2*sqrt(35) + 14*sin(x)/(1 + cos(x))))/35
Combinatoria
[src]
/ ____ \
____ | 2*\/ 35 14*sin(x) |
\/ 35 *log|- --------------------- + ----------------------------------------------------------|
| ____ 14*sin(x) ____ ____ 14*sin(x) 14*cos(x)*sin(x)|
| 2*\/ 35 + ---------- 2*\/ 35 + 2*\/ 35 *cos(x) + ---------- + ----------------|
\ 1 + cos(x) 1 + cos(x) 1 + cos(x) /
------------------------------------------------------------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{14 \sin{\left(x \right)}}{2 \sqrt{35} \cos{\left(x \right)} + 2 \sqrt{35} + \frac{14 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} - \frac{2 \sqrt{35}}{2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{35}$$
sqrt(35)*log(-2*sqrt(35)/(2*sqrt(35) + 14*sin(x)/(1 + cos(x))) + 14*sin(x)/(2*sqrt(35) + 2*sqrt(35)*cos(x) + 14*sin(x)/(1 + cos(x)) + 14*cos(x)*sin(x)/(1 + cos(x))))/35
Compilar la expresión
[src]
/14*sin(x) ____\
|---------- - 2*\/ 35 |
____ |1 + cos(x) |
\/ 35 *log|---------------------|
| ____ 14*sin(x) |
|2*\/ 35 + ----------|
\ 1 + cos(x)/
---------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{35}$$
sqrt(35)*log(((14*sin(x))/(1 + cos(x)) - 2*sqrt(35))/(2*sqrt(35) + (14*sin(x))/(1 + cos(x))))/35
Parte trigonométrica
[src]
/ /x\ \
| 28*tan|-| |
| ____ \2/ |
|- 2*\/ 35 + -------------------------------|
| / 2/x\\|
| | 1 - tan |-|||
| / 2/x\\ | \2/||
| |1 + tan |-||*|1 + -----------||
| \ \2// | 2/x\||
| | 1 + tan |-|||
____ | \ \2//|
\/ 35 *log|--------------------------------------------|
| /x\ |
| 28*tan|-| |
| ____ \2/ |
| 2*\/ 35 + ------------------------------- |
| / 2/x\\ |
| | 1 - tan |-|| |
| / 2/x\\ | \2/| |
| |1 + tan |-||*|1 + -----------| |
| \ \2// | 2/x\| |
| | 1 + tan |-|| |
\ \ \2// /
--------------------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{28 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}}{2 \sqrt{35} + \frac{28 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}} \right)}}{35}$$
/ ____ 14 \
|- 2*\/ 35 + ------------------------|
| / 1 \ |
| |1 + -----------|*csc(x)|
| | /pi \| |
| | csc|-- - x|| |
____ | \ \2 // |
\/ 35 *log|-------------------------------------|
| ____ 14 |
| 2*\/ 35 + ------------------------ |
| / 1 \ |
| |1 + -----------|*csc(x) |
| | /pi \| |
| | csc|-- - x|| |
\ \ \2 // /
-------------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{14}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}}{2 \sqrt{35} + \frac{14}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}} \right)}}{35}$$
/ /x\ \
| 28*cot|-| |
| ____ \2/ |
|- 2*\/ 35 + --------------------------------|
| / 2/x\\|
| | -1 + cot |-|||
| / 2/x\\ | \2/||
| |1 + cot |-||*|1 + ------------||
| \ \2// | 2/x\ ||
| | 1 + cot |-| ||
____ | \ \2/ /|
\/ 35 *log|---------------------------------------------|
| /x\ |
| 28*cot|-| |
| ____ \2/ |
| 2*\/ 35 + -------------------------------- |
| / 2/x\\ |
| | -1 + cot |-|| |
| / 2/x\\ | \2/| |
| |1 + cot |-||*|1 + ------------| |
| \ \2// | 2/x\ | |
| | 1 + cot |-| | |
\ \ \2/ / /
---------------------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{28 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}}{2 \sqrt{35} + \frac{28 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}} \right)}}{35}$$
/ / pi\\
| 14*cos|x - --||
| ____ \ 2 /|
|- 2*\/ 35 + --------------|
____ | 1 + cos(x) |
\/ 35 *log|---------------------------|
| / pi\ |
| 14*cos|x - --| |
| ____ \ 2 / |
| 2*\/ 35 + -------------- |
\ 1 + cos(x) /
---------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{14 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1}}{2 \sqrt{35} + \frac{14 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1}} \right)}}{35}$$
/ ____ 14*sin(x) \
|- 2*\/ 35 + ---------------|
| / pi\|
| 1 + sin|x + --||
____ | \ 2 /|
\/ 35 *log|----------------------------|
| ____ 14*sin(x) |
| 2*\/ 35 + --------------- |
| / pi\ |
| 1 + sin|x + --| |
\ \ 2 / /
----------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1}}{2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1}} \right)}}{35}$$
/ ____ 14 \
|- 2*\/ 35 + -------------------|
| / 1 \ |
| |1 + ------|*csc(x)|
____ | \ sec(x)/ |
\/ 35 *log|--------------------------------|
| ____ 14 |
| 2*\/ 35 + ------------------- |
| / 1 \ |
| |1 + ------|*csc(x) |
\ \ sec(x)/ /
--------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{14}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}}}{2 \sqrt{35} + \frac{14}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}}} \right)}}{35}$$
/ ____ 14 \
|- 2*\/ 35 + ------------------------|
| / 1 \ / pi\|
| |1 + ------|*sec|x - --||
____ | \ sec(x)/ \ 2 /|
\/ 35 *log|-------------------------------------|
| ____ 14 |
| 2*\/ 35 + ------------------------ |
| / 1 \ / pi\ |
| |1 + ------|*sec|x - --| |
\ \ sec(x)/ \ 2 / /
-------------------------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{14}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}}{2 \sqrt{35} + \frac{14}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}} \right)}}{35}$$
/ ____ 14*sin(x) \
|- 2*\/ 35 + ----------|
____ | 1 + cos(x)|
\/ 35 *log|-----------------------|
| ____ 14*sin(x) |
| 2*\/ 35 + ---------- |
\ 1 + cos(x) /
-----------------------------------
35
$$\frac{\sqrt{35} \log{\left(\frac{- 2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{2 \sqrt{35} + \frac{14 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{35}$$
sqrt(35)*log((-2*sqrt(35) + 14*sin(x)/(1 + cos(x)))/(2*sqrt(35) + 14*sin(x)/(1 + cos(x))))/35