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Expression simplification/ Least common denominator/ log((7*sin(x))/(1+cos(x))+3)/7

Least common denominator log((7*sin(x))/(1+cos(x))+3)/7

An expression to simplify:

The solution

You have entered [src] 
   / 7*sin(x)     \
log|---------- + 3|
   \1 + cos(x)    /
-------------------
         7
$$\frac{\log{\left(3 + \frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)}}{7}$$ 
log((7*sin(x))/(1 + cos(x)) + 3)/7
Fraction decomposition [src] 
log((7*sin(x))/(1 + cos(x)) + 3)/7
$$\frac{\log{\left(3 + \frac{7 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1} \right)}}{7}$$ 
   / 7*sin(x)     \
log|---------- + 3|
   \1 + cos(x)    /
-------------------
         7
General simplification [src] 
   /3 + 3*cos(x) + 7*sin(x)\
log|-----------------------|
   \       1 + cos(x)      /
----------------------------
             7
$$\frac{\log{\left(\frac{7 \sin{\left(x \right)} + 3 \cos{\left(x \right)} + 3}{\cos{\left(x \right)} + 1} \right)}}{7}$$ 
log((3 + 3*cos(x) + 7*sin(x))/(1 + cos(x)))/7
Numerical answer [src] 
0.142857142857143*log((7*sin(x))/(1 + cos(x)) + 3)
0.142857142857143*log((7*sin(x))/(1 + cos(x)) + 3)
Rational denominator [src] 
   /3 + 3*cos(x) + 7*sin(x)\
log|-----------------------|
   \       1 + cos(x)      /
----------------------------
             7
$$\frac{\log{\left(\frac{7 \sin{\left(x \right)} + 3 \cos{\left(x \right)} + 3}{\cos{\left(x \right)} + 1} \right)}}{7}$$ 
log((3 + 3*cos(x) + 7*sin(x))/(1 + cos(x)))/7
Powers [src] 
   /        /   -I*x    I*x\\
   |    7*I*\- e     + e   /|
log|3 - --------------------|
   |      /     I*x    -I*x\|
   |      |    e      e    ||
   |    2*|1 + ---- + -----||
   \      \     2       2  //
-----------------------------
              7
$$\frac{\log{\left(- \frac{7 i \left(e^{i x} - e^{- i x}\right)}{2 \left(\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}\right)} + 3 \right)}}{7}$$ 
log(3 - 7*i*(-exp(-i*x) + exp(i*x))/(2*(1 + exp(i*x)/2 + exp(-i*x)/2)))/7
Combining rational expressions [src] 
   /3 + 3*cos(x) + 7*sin(x)\
log|-----------------------|
   \       1 + cos(x)      /
----------------------------
             7
$$\frac{\log{\left(\frac{7 \sin{\left(x \right)} + 3 \cos{\left(x \right)} + 3}{\cos{\left(x \right)} + 1} \right)}}{7}$$ 
log((3 + 3*cos(x) + 7*sin(x))/(1 + cos(x)))/7
Trigonometric part [src] 
   /         /    pi\\
   |    7*cos|x - --||
   |         \    2 /|
log|3 + -------------|
   \      1 + cos(x) /
----------------------
          7
$$\frac{\log{\left(3 + \frac{7 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1} \right)}}{7}$$ 
   /                     /x\            \
   |               14*cot|-|            |
   |                     \2/            |
log|3 + --------------------------------|
   |                  /            2/x\\|
   |                  |    -1 + cot |-|||
   |    /       2/x\\ |             \2/||
   |    |1 + cot |-||*|1 + ------------||
   |    \        \2// |           2/x\ ||
   |                  |    1 + cot |-| ||
   \                  \            \2/ //
-----------------------------------------
                    7
$$\frac{\log{\left(3 + \frac{14 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{7}$$ 
   /               7            \
log|3 + ------------------------|
   |    /      1   \    /    pi\|
   |    |1 + ------|*sec|x - --||
   \    \    sec(x)/    \    2 //
---------------------------------
                7
$$\frac{\log{\left(3 + \frac{7}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{7}$$ 
   /               7            \
log|3 + ------------------------|
   |    /         1     \       |
   |    |1 + -----------|*csc(x)|
   |    |       /pi    \|       |
   |    |    csc|-- - x||       |
   \    \       \2     //       /
---------------------------------
                7
$$\frac{\log{\left(3 + \frac{7}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} \right)}}{7}$$ 
   /                     /x\           \
   |               14*tan|-|           |
   |                     \2/           |
log|3 + -------------------------------|
   |                  /           2/x\\|
   |                  |    1 - tan |-|||
   |    /       2/x\\ |            \2/||
   |    |1 + tan |-||*|1 + -----------||
   |    \        \2// |           2/x\||
   |                  |    1 + tan |-|||
   \                  \            \2///
----------------------------------------
                   7
$$\frac{\log{\left(3 + \frac{14 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{7}$$ 
   /        7*sin(x)   \
log|3 + ---------------|
   |           /    pi\|
   |    1 + sin|x + --||
   \           \    2 //
------------------------
           7
$$\frac{\log{\left(3 + \frac{7 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1} \right)}}{7}$$ 
   /             7         \
log|3 + -------------------|
   |    /      1   \       |
   |    |1 + ------|*csc(x)|
   \    \    sec(x)/       /
----------------------------
             7
$$\frac{\log{\left(3 + \frac{7}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}} \right)}}{7}$$ 
log(3 + 7/((1 + 1/sec(x))*csc(x)))/7
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