Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(x)/(2+2*tan(x)^2)+tan(x)-(3*x)/2
¿Cómo vas a descomponer esta tan(x)/(2+2*tan(x)^2)+tan(x)-(3*x)/2 expresión en fracciones?
Solución
Ha introducido
[src]
tan(x) 3*x
------------- + tan(x) - ---
2 2
2 + 2*tan (x)
$$- \frac{3 x}{2} + \left(\tan{\left(x \right)} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}\right)$$
tan(x)/(2 + 2*tan(x)^2) + tan(x) - 3*x/2
Simplificación general
[src]
3*x sin(2*x) - --- + -------- + tan(x) 2 4
$$- \frac{3 x}{2} + \frac{\sin{\left(2 x \right)}}{4} + \tan{\left(x \right)}$$
-3*x/2 + sin(2*x)/4 + tan(x)
Respuesta numérica
[src]
-1.5*x + tan(x)/(2.0 + 2.0*tan(x)^2) + tan(x)
-1.5*x + tan(x)/(2.0 + 2.0*tan(x)^2) + tan(x)
Unión de expresiones racionales
[src]
/ 2 \ / 2 \
\3 + 2*tan (x)/*tan(x) - 3*x*\1 + tan (x)/
------------------------------------------
/ 2 \
2*\1 + tan (x)/
$$\frac{- 3 x \left(\tan^{2}{\left(x \right)} + 1\right) + \left(2 \tan^{2}{\left(x \right)} + 3\right) \tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)}$$
((3 + 2*tan(x)^2)*tan(x) - 3*x*(1 + tan(x)^2))/(2*(1 + tan(x)^2))
Combinatoria
[src]
/ 3 2 \
-\-3*tan(x) - 2*tan (x) + 3*x + 3*x*tan (x)/
---------------------------------------------
/ 2 \
2*\1 + tan (x)/
$$- \frac{3 x \tan^{2}{\left(x \right)} + 3 x - 2 \tan^{3}{\left(x \right)} - 3 \tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)}$$
-(-3*tan(x) - 2*tan(x)^3 + 3*x + 3*x*tan(x)^2)/(2*(1 + tan(x)^2))
Potencias
[src]
3*x tan(x)
- --- + ------------- + tan(x)
2 2
2 + 2*tan (x)
$$- \frac{3 x}{2} + \tan{\left(x \right)} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}$$
/ I*x -I*x\ / I*x -I*x\
3*x I*\- e + e / I*\- e + e /
- --- + ------------------ + ----------------------------------------
2 I*x -I*x / 2\
e + e | / I*x -I*x\ |
| 2*\- e + e / | / I*x -I*x\
|2 - -------------------|*\e + e /
| 2 |
| / I*x -I*x\ |
\ \e + e / /
$$- \frac{3 x}{2} + \frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} + \frac{i \left(- e^{i x} + e^{- i x}\right)}{\left(- \frac{2 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 2\right) \left(e^{i x} + e^{- i x}\right)}$$
-3*x/2 + i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)) + i*(-exp(i*x) + exp(-i*x))/((2 - 2*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x)))
Denominador racional
[src]
/ 2 \ / 2 \
2*tan(x) - 3*x*\2 + 2*tan (x)/ + 2*\2 + 2*tan (x)/*tan(x)
---------------------------------------------------------
2
4 + 4*tan (x)
$$\frac{- 3 x \left(2 \tan^{2}{\left(x \right)} + 2\right) + 2 \left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)} + 2 \tan{\left(x \right)}}{4 \tan^{2}{\left(x \right)} + 4}$$
(2*tan(x) - 3*x*(2 + 2*tan(x)^2) + 2*(2 + 2*tan(x)^2)*tan(x))/(4 + 4*tan(x)^2)
Denominador común
[src]
3*x tan(x)
- --- + ------------- + tan(x)
2 2
2 + 2*tan (x)
$$- \frac{3 x}{2} + \tan{\left(x \right)} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}$$
-3*x/2 + tan(x)/(2 + 2*tan(x)^2) + tan(x)
Compilar la expresión
[src]
3*x tan(x)
- --- + ------------- + tan(x)
2 2
2 + 2*tan (x)
$$- \frac{3 x}{2} + \tan{\left(x \right)} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}$$
-3*x/2 + tan(x)/(2 + 2*tan(x)^2) + tan(x)
Parte trigonométrica
[src]
2 2
3*x 2*sin (x) 2*sin (x)
- --- + --------- + ------------------------
2 sin(2*x) / 4 \
| 8*sin (x)|
|2 + ---------|*sin(2*x)
| 2 |
\ sin (2*x)/
$$- \frac{3 x}{2} + \frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + \frac{2 \sin^{2}{\left(x \right)}}{\left(\frac{8 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 2\right) \sin{\left(2 x \right)}}$$
3*x sin(2*x) - --- + -------- + tan(x) 2 4
$$- \frac{3 x}{2} + \frac{\sin{\left(2 x \right)}}{4} + \tan{\left(x \right)}$$
3*x sec(x) sec(x)
- --- + ------ + ----------------------
2 csc(x) / 2 \
| 2*sec (x)|
|2 + ---------|*csc(x)
| 2 |
\ csc (x) /
$$- \frac{3 x}{2} + \frac{\sec{\left(x \right)}}{\csc{\left(x \right)}} + \frac{\sec{\left(x \right)}}{\left(2 + \frac{2 \sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}$$
3*x sin(x) sin(x)
- --- + ------ + ----------------------
2 cos(x) / 2 \
| 2*sin (x)|
|2 + ---------|*cos(x)
| 2 |
\ cos (x) /
$$- \frac{3 x}{2} + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\sin{\left(x \right)}}{\left(\frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right) \cos{\left(x \right)}}$$
3*x tan(x)
- --- + --------------- + tan(x)
2 / 2 \
2*\1 + tan (x)/
$$- \frac{3 x}{2} + \tan{\left(x \right)} + \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)}$$
2 3*x sin(2*x) 2*sin (x) - --- + -------- + --------- 2 4 sin(2*x)
$$- \frac{3 x}{2} + \frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} + \frac{\sin{\left(2 x \right)}}{4}$$
3*x 1 sec(x)
- --- + --------------- + -----------
2 / pi\ / pi\
4*sec|2*x - --| sec|x - --|
\ 2 / \ 2 /
$$- \frac{3 x}{2} + \frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
3*x sec(x) sec(x)
- --- + ----------- + ------------------------------
2 / pi\ / 2 \
sec|x - --| | 2*sec (x) | / pi\
\ 2 / |2 + ------------|*sec|x - --|
| 2/ pi\| \ 2 /
| sec |x - --||
\ \ 2 //
$$- \frac{3 x}{2} + \frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{\sec{\left(x \right)}}{\left(\frac{2 \sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 2\right) \sec{\left(x - \frac{\pi}{2} \right)}}$$
/pi \ /pi \
csc|-- - x| csc|-- - x|
3*x \2 / \2 /
- --- + ----------- + ---------------------------
2 csc(x) / 2/pi \\
| 2*csc |-- - x||
| \2 /|
|2 + --------------|*csc(x)
| 2 |
\ csc (x) /
$$- \frac{3 x}{2} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\left(2 + \frac{2 \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}$$
1 3*x 1
------ - --- + --------------------
cot(x) 2 / 2 \
|2 + -------|*cot(x)
| 2 |
\ cot (x)/
$$- \frac{3 x}{2} + \frac{1}{\cot{\left(x \right)}} + \frac{1}{\left(2 + \frac{2}{\cot^{2}{\left(x \right)}}\right) \cot{\left(x \right)}}$$
/ pi\ / pi\
cos|2*x - --| cos|x - --|
3*x \ 2 / \ 2 /
- --- + ------------- + -----------
2 4 cos(x)
$$- \frac{3 x}{2} + \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}$$
3*x tan(x)
- --- + ------------- + tan(x)
2 2
2 + 2*tan (x)
$$- \frac{3 x}{2} + \tan{\left(x \right)} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}$$
/ pi\ / pi\
cos|x - --| cos|x - --|
3*x \ 2 / \ 2 /
- --- + ----------- + ---------------------------
2 cos(x) / 2/ pi\\
| 2*cos |x - --||
| \ 2 /|
|2 + --------------|*cos(x)
| 2 |
\ cos (x) /
$$- \frac{3 x}{2} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\left(2 + \frac{2 \cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}$$
1 3*x cot(x)
------ - --- + ---------------
cot(x) 2 / 2 \
2*\1 + cot (x)/
$$- \frac{3 x}{2} + \frac{1}{\cot{\left(x \right)}} + \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)}$$
/pi \
csc|-- - x|
3*x 1 \2 /
- --- + ---------- + -----------
2 4*csc(2*x) csc(x)
$$- \frac{3 x}{2} + \frac{1}{4 \csc{\left(2 x \right)}} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}$$
-3*x/2 + 1/(4*csc(2*x)) + csc(pi/2 - x)/csc(x)