Descomposición de una fracción
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sqrt(3)*atan(sin(x)/(sqrt(3) + sqrt(3)*cos(x)))/6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{\sqrt{3} \cos{\left(x \right)} + \sqrt{3}} \right)}}{6}$$
___ / sin(x) \
\/ 3 *atan|--------------------|
| ___ ___ |
\\/ 3 + \/ 3 *cos(x)/
--------------------------------
6
/ ___ \
___ | \/ 3 *sin(x) |
\/ 3 *atan|--------------|
\3*(1 + cos(x))/
--------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \sin{\left(x \right)}}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{6}$$
/ ___ / -I*x I*x\\
___ |I*\/ 3 *\- e + e /|
-\/ 3 *atan|------------------------|
| / I*x -I*x\ |
| | e e | |
| 6*|1 + ---- + -----| |
\ \ 2 2 / /
--------------------------------------
6
$$- \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} i \left(e^{i x} - e^{- i x}\right)}{6 \left(\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}\right)} \right)}}{6}$$
-sqrt(3)*atan(i*sqrt(3)*(-exp(-i*x) + exp(i*x))/(6*(1 + exp(i*x)/2 + exp(-i*x)/2)))/6
Unión de expresiones racionales
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/ ___ \
___ | \/ 3 *sin(x) |
\/ 3 *atan|--------------|
\3*(1 + cos(x))/
--------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \sin{\left(x \right)}}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{6}$$
sqrt(3)*atan(sqrt(3)*sin(x)/(3*(1 + cos(x))))/6
Abrimos la expresión
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/ ___ \
___ | \/ 3 *sin(x) |
\/ 3 *atan|--------------|
\3*(1 + cos(x))/
--------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \sin{\left(x \right)}}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{6}$$
___
\/ 3 / sin(x) \
-----*atan|--------------------|
6 | ___ ___ |
\\/ 3 + \/ 3 *cos(x)/
$$\frac{\sqrt{3}}{6} \operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{\sqrt{3} \cos{\left(x \right)} + \sqrt{3}} \right)}$$
(sqrt(3)/6)*atan(sin(x)/(sqrt(3) + sqrt(3)*cos(x)))
Parte trigonométrica
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/ ___ \
___ | \/ 3 |
\/ 3 *atan|--------------------------|
| / 1 \ |
|3*|1 + -----------|*csc(x)|
| | /pi \| |
| | csc|-- - x|| |
\ \ \2 // /
--------------------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3 \left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} \right)}}{6}$$
/ ___ \
___ | \/ 3 *sin(x) |
\/ 3 *atan|-------------------|
| / / pi\\|
|3*|1 + sin|x + --|||
\ \ \ 2 ///
-------------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \sin{\left(x \right)}}{3 \left(\sin{\left(x + \frac{\pi}{2} \right)} + 1\right)} \right)}}{6}$$
/ ___ \
___ | \/ 3 |
\/ 3 *atan|--------------------------|
| / 1 \ / pi\|
|3*|1 + ------|*sec|x - --||
\ \ sec(x)/ \ 2 //
--------------------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3 \left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{6}$$
/ ___ \
___ | \/ 3 |
\/ 3 *atan|---------------------|
| / 1 \ |
|3*|1 + ------|*csc(x)|
\ \ sec(x)/ /
---------------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3}}{3 \left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}} \right)}}{6}$$
/ ___ /x\ \
| 2*\/ 3 *cot|-| |
___ | \2/ |
\/ 3 *atan|----------------------------------|
| / 2/x\\|
| | -1 + cot |-|||
| / 2/x\\ | \2/||
|3*|1 + cot |-||*|1 + ------------||
| \ \2// | 2/x\ ||
| | 1 + cot |-| ||
\ \ \2/ //
----------------------------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \cot{\left(\frac{x}{2} \right)}}{3 \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{6}$$
/ ___ / pi\\
|\/ 3 *cos|x - --||
___ | \ 2 /|
\/ 3 *atan|-----------------|
\ 3*(1 + cos(x)) /
-----------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \cos{\left(x - \frac{\pi}{2} \right)}}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{6}$$
/ ___ \
___ | \/ 3 *sin(x) |
\/ 3 *atan|--------------|
\3*(1 + cos(x))/
--------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \sin{\left(x \right)}}{3 \left(\cos{\left(x \right)} + 1\right)} \right)}}{6}$$
/ ___ /x\ \
| 2*\/ 3 *tan|-| |
___ | \2/ |
\/ 3 *atan|---------------------------------|
| / 2/x\\|
| | 1 - tan |-|||
| / 2/x\\ | \2/||
|3*|1 + tan |-||*|1 + -----------||
| \ \2// | 2/x\||
| | 1 + tan |-|||
\ \ \2///
---------------------------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3 \left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{6}$$
___ / sin(x) \
\/ 3 *atan|------------------|
| ___ |
\\/ 3 *(1 + cos(x))/
------------------------------
6
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{\sqrt{3} \left(\cos{\left(x \right)} + 1\right)} \right)}}{6}$$
sqrt(3)*atan(sin(x)/((sqrt(3)*(1 + cos(x)))))/6