Sr Examen
¿Cómo vas a descomponer esta (2tg6x)/(1+tg^26x) expresión en fracciones?
Solución
Ha introducido
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2*tan(6*x)
------------
26
1 + tan (x)
$$\frac{2 \tan{\left(6 x \right)}}{\tan^{26}{\left(x \right)} + 1}$$
(2*tan(6*x))/(1 + tan(x)^26)
Combinatoria
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2*tan(6*x) ------------------------------------------------------------------------------------------------------------------------------------------------- / 2 \ / 4 8 12 16 20 24 2 6 10 14 18 22 \ \1 + tan (x)/*\1 + tan (x) + tan (x) + tan (x) + tan (x) + tan (x) + tan (x) - tan (x) - tan (x) - tan (x) - tan (x) - tan (x) - tan (x)/
$$\frac{2 \tan{\left(6 x \right)}}{\left(\tan^{2}{\left(x \right)} + 1\right) \left(\tan^{24}{\left(x \right)} - \tan^{22}{\left(x \right)} + \tan^{20}{\left(x \right)} - \tan^{18}{\left(x \right)} + \tan^{16}{\left(x \right)} - \tan^{14}{\left(x \right)} + \tan^{12}{\left(x \right)} - \tan^{10}{\left(x \right)} + \tan^{8}{\left(x \right)} - \tan^{6}{\left(x \right)} + \tan^{4}{\left(x \right)} - \tan^{2}{\left(x \right)} + 1\right)}$$
2*tan(6*x)/((1 + tan(x)^2)*(1 + tan(x)^4 + tan(x)^8 + tan(x)^12 + tan(x)^16 + tan(x)^20 + tan(x)^24 - tan(x)^2 - tan(x)^6 - tan(x)^10 - tan(x)^14 - tan(x)^18 - tan(x)^22))
Potencias
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/ 6*I*x -6*I*x\
2*I*\- e + e /
-------------------------------------------
/ 26\
| / I*x -I*x\ |
| \- e + e / | / -6*I*x 6*I*x\
|1 - ------------------|*\e + e /
| 26 |
| / I*x -I*x\ |
\ \e + e / /
$$\frac{2 i \left(- e^{6 i x} + e^{- 6 i x}\right)}{\left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{26}}{\left(e^{i x} + e^{- i x}\right)^{26}} + 1\right) \left(e^{6 i x} + e^{- 6 i x}\right)}$$
2*i*(-exp(6*i*x) + exp(-6*i*x))/((1 - (-exp(i*x) + exp(-i*x))^26/(exp(i*x) + exp(-i*x))^26)*(exp(-6*i*x) + exp(6*i*x)))
Parte trigonométrica
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2
4*sin (6*x)
---------------------------------
/ 52 \
| 67108864*sin (x)|
|1 + -----------------|*sin(12*x)
| 26 |
\ sin (2*x) /
$$\frac{4 \sin^{2}{\left(6 x \right)}}{\left(\frac{67108864 \sin^{52}{\left(x \right)}}{\sin^{26}{\left(2 x \right)}} + 1\right) \sin{\left(12 x \right)}}$$
2*sec(6*x) --------------------------------- / 26 \ | sec (x) | / pi\ |1 + -------------|*sec|6*x - --| | 26/ pi\| \ 2 / | sec |x - --|| \ \ 2 //
$$\frac{2 \sec{\left(6 x \right)}}{\left(\frac{\sec^{26}{\left(x \right)}}{\sec^{26}{\left(x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(6 x - \frac{\pi}{2} \right)}}$$
/ pi\
2*cos|6*x - --|
\ 2 /
----------------------------
/ 26/ pi\\
| cos |x - --||
| \ 2 /|
|1 + -------------|*cos(6*x)
| 26 |
\ cos (x) /
$$\frac{2 \cos{\left(6 x - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{26}{\left(x - \frac{\pi}{2} \right)}}{\cos^{26}{\left(x \right)}}\right) \cos{\left(6 x \right)}}$$
2*sin(6*x) ----------------------- / 26 \ | sin (x)| |1 + --------|*cos(6*x) | 26 | \ cos (x)/
$$\frac{2 \sin{\left(6 x \right)}}{\left(\frac{\sin^{26}{\left(x \right)}}{\cos^{26}{\left(x \right)}} + 1\right) \cos{\left(6 x \right)}}$$
2*sec(6*x) ----------------------- / 26 \ | sec (x)| |1 + --------|*csc(6*x) | 26 | \ csc (x)/
$$\frac{2 \sec{\left(6 x \right)}}{\left(1 + \frac{\sec^{26}{\left(x \right)}}{\csc^{26}{\left(x \right)}}\right) \csc{\left(6 x \right)}}$$
2 ----------------------- / 1 \ |1 + --------|*cot(6*x) | 26 | \ cot (x)/
$$\frac{2}{\left(1 + \frac{1}{\cot^{26}{\left(x \right)}}\right) \cot{\left(6 x \right)}}$$
/pi \
2*csc|-- - 6*x|
\2 /
----------------------------
/ 26/pi \\
| csc |-- - x||
| \2 /|
|1 + -------------|*csc(6*x)
| 26 |
\ csc (x) /
$$\frac{2 \csc{\left(- 6 x + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{26}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{26}{\left(x \right)}}\right) \csc{\left(6 x \right)}}$$
2*csc(pi/2 - 6*x)/((1 + csc(pi/2 - x)^26/csc(x)^26)*csc(6*x))