Descomposición de una fracción
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sqrt(5)*atan(sqrt(5)/5 + 3*sqrt(5)*sin(x)/(5*(1 + cos(x))))/5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} + \frac{3 \sqrt{5} \sin{\left(x \right)}}{5 \left(\cos{\left(x \right)} + 1\right)} \right)}}{5}$$
/ ___ ___ \
___ |\/ 5 3*\/ 5 *sin(x)|
\/ 5 *atan|----- + --------------|
\ 5 5*(1 + cos(x))/
----------------------------------
5
Simplificación general
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/ ___ \
___ |\/ 5 *(1 + 3*sin(x) + cos(x))|
\/ 5 *atan|-----------------------------|
\ 5*(1 + cos(x)) /
-----------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(3 \sin{\left(x \right)} + \cos{\left(x \right)} + 1\right)}{5 \left(\cos{\left(x \right)} + 1\right)} \right)}}{5}$$
sqrt(5)*atan(sqrt(5)*(1 + 3*sin(x) + cos(x))/(5*(1 + cos(x))))/5
/ ___ ___ \
___ |\/ 5 3*\/ 5 *sin(x)|
\/ 5 *atan|----- + --------------|
\ 5 5*(1 + cos(x))/
----------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} + \frac{3 \sqrt{5} \sin{\left(x \right)}}{5 \left(\cos{\left(x \right)} + 1\right)} \right)}}{5}$$
sqrt(5)*atan(sqrt(5)/5 + 3*sqrt(5)*sin(x)/(5*(1 + cos(x))))/5
Unión de expresiones racionales
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/ ___ \
___ |\/ 5 *(1 + 3*sin(x) + cos(x))|
\/ 5 *atan|-----------------------------|
\ 5*(1 + cos(x)) /
-----------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(3 \sin{\left(x \right)} + \cos{\left(x \right)} + 1\right)}{5 \left(\cos{\left(x \right)} + 1\right)} \right)}}{5}$$
sqrt(5)*atan(sqrt(5)*(1 + 3*sin(x) + cos(x))/(5*(1 + cos(x))))/5
Denominador racional
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/ ___ \
___ |\/ 5 *(1 + 3*sin(x) + cos(x))|
\/ 5 *atan|-----------------------------|
\ 5*(1 + cos(x)) /
-----------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(3 \sin{\left(x \right)} + \cos{\left(x \right)} + 1\right)}{5 \left(\cos{\left(x \right)} + 1\right)} \right)}}{5}$$
sqrt(5)*atan(sqrt(5)*(1 + 3*sin(x) + cos(x))/(5*(1 + cos(x))))/5
/ ___ ___ \
___ |\/ 5 3*\/ 5 *sin(x)|
\/ 5 *atan|----- + --------------|
\ 5 5*(1 + cos(x))/
----------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} + \frac{3 \sqrt{5} \sin{\left(x \right)}}{5 \left(\cos{\left(x \right)} + 1\right)} \right)}}{5}$$
sqrt(5)*atan(sqrt(5)/5 + 3*sqrt(5)*sin(x)/(5*(1 + cos(x))))/5
Abrimos la expresión
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/ ___ / 6*sin(x) \\
___ |\/ 5 *|---------- + 2||
\/ 5 | \1 + cos(x) /|
-----*atan|----------------------|
5 \ 10 /
$$\frac{\sqrt{5}}{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)}{10} \right)}$$
___ / ___ ___ \
\/ 5 |\/ 5 3*\/ 5 *sin(x)|
-----*atan|----- + --------------|
5 \ 5 5*(1 + cos(x))/
$$\frac{\sqrt{5}}{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} + \frac{3 \sqrt{5} \sin{\left(x \right)}}{5 \left(\cos{\left(x \right)} + 1\right)} \right)}$$
(sqrt(5)/5)*atan(sqrt(5)/5 + 3*sqrt(5)*sin(x)/(5*(1 + cos(x))))
Compilar la expresión
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/ 6*sin(x) \
|---------- + 2|
___ |1 + cos(x) |
\/ 5 *atan|--------------|
| ___ |
\ 2*\/ 5 /
--------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{2 + \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{2 \sqrt{5}} \right)}}{5}$$
sqrt(5)*atan(((6*sin(x))/(1 + cos(x)) + 2)/((2*sqrt(5))))/5
Parte trigonométrica
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/ ___ / 6*sin(x) \\
|\/ 5 *|2 + ---------------||
| | / pi\||
| | 1 + sin|x + --|||
___ | \ \ 2 //|
\/ 5 *atan|---------------------------|
\ 10 /
---------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{6 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1}\right)}{10} \right)}}{5}$$
/ / / pi\\\
| | 6*cos|x - --|||
| ___ | \ 2 /||
|\/ 5 *|2 + -------------||
___ | \ 1 + cos(x) /|
\/ 5 *atan|-------------------------|
\ 10 /
-------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{6 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1}\right)}{10} \right)}}{5}$$
/ ___ / 6 \\
|\/ 5 *|2 + ------------------------||
| | / 1 \ ||
| | |1 + -----------|*csc(x)||
| | | /pi \| ||
| | | csc|-- - x|| ||
___ | \ \ \2 // /|
\/ 5 *atan|------------------------------------|
\ 10 /
------------------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{6}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}\right)}{10} \right)}}{5}$$
/ ___ / 6 \\
|\/ 5 *|2 + -------------------||
| | / 1 \ ||
| | |1 + ------|*csc(x)||
___ | \ \ sec(x)/ /|
\/ 5 *atan|-------------------------------|
\ 10 /
-------------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{6}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}}\right)}{10} \right)}}{5}$$
/ ___ / 6 \\
|\/ 5 *|2 + ------------------------||
| | / 1 \ / pi\||
| | |1 + ------|*sec|x - --|||
___ | \ \ sec(x)/ \ 2 //|
\/ 5 *atan|------------------------------------|
\ 10 /
------------------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{6}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}\right)}{10} \right)}}{5}$$
/ / /x\ \\
| | 12*tan|-| ||
| ___ | \2/ ||
|\/ 5 *|2 + -------------------------------||
| | / 2/x\\||
| | | 1 - tan |-||||
| | / 2/x\\ | \2/|||
| | |1 + tan |-||*|1 + -----------|||
| | \ \2// | 2/x\|||
| | | 1 + tan |-||||
___ | \ \ \2///|
\/ 5 *atan|-------------------------------------------|
\ 10 /
-------------------------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{12 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right)}{10} \right)}}{5}$$
/ / /x\ \\
| | 12*cot|-| ||
| ___ | \2/ ||
|\/ 5 *|2 + --------------------------------||
| | / 2/x\\||
| | | -1 + cot |-||||
| | / 2/x\\ | \2/|||
| | |1 + cot |-||*|1 + ------------|||
| | \ \2// | 2/x\ |||
| | | 1 + cot |-| |||
___ | \ \ \2/ //|
\/ 5 *atan|--------------------------------------------|
\ 10 /
--------------------------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{12 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right)}{10} \right)}}{5}$$
/ ___ / 6*sin(x) \\
|\/ 5 *|2 + ----------||
___ | \ 1 + cos(x)/|
\/ 5 *atan|----------------------|
\ 10 /
----------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)}{10} \right)}}{5}$$
sqrt(5)*atan(sqrt(5)*(2 + 6*sin(x)/(1 + cos(x)))/10)/5
/ / / -I*x I*x\\\
| ___ | 3*I*\- e + e /||
|\/ 5 *|2 - --------------------||
| | I*x -I*x ||
| | e e ||
| | 1 + ---- + ----- ||
___ | \ 2 2 /|
\/ 5 *atan|--------------------------------|
\ 10 /
--------------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(- \frac{3 i \left(e^{i x} - e^{- i x}\right)}{\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}} + 2\right)}{10} \right)}}{5}$$
/ ___ / 6*sin(x) \\
|\/ 5 *|2 + ----------||
___ | \ 1 + cos(x)/|
\/ 5 *atan|----------------------|
\ 10 /
----------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} \left(2 + \frac{6 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)}{10} \right)}}{5}$$
___ / ___ /1 3*sin(x) \\
\/ 5 *atan|\/ 5 *|- + --------------||
\ \5 5*(1 + cos(x))//
--------------------------------------
5
$$\frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} \left(\frac{1}{5} + \frac{3 \sin{\left(x \right)}}{5 \left(\cos{\left(x \right)} + 1\right)}\right) \right)}}{5}$$
sqrt(5)*atan(sqrt(5)*(1/5 + 3*sin(x)/(5*(1 + cos(x)))))/5