Simplificación general
[src]
(8 + 8*x)*(x - sin(2*x)) + sin(4*x)
-----------------------------------
32*(1 + x)
$$\frac{\left(x - \sin{\left(2 x \right)}\right) \left(8 x + 8\right) + \sin{\left(4 x \right)}}{32 \left(x + 1\right)}$$
((8 + 8*x)*(x - sin(2*x)) + sin(4*x))/(32*(1 + x))
Denominador racional
[src]
4*sin(4*x) + x*(32 + 32*x) - 2*(16 + 16*x)*sin(2*x)
---------------------------------------------------
128 + 128*x
$$\frac{x \left(32 x + 32\right) - 2 \left(16 x + 16\right) \sin{\left(2 x \right)} + 4 \sin{\left(4 x \right)}}{128 x + 128}$$
(4*sin(4*x) + x*(32 + 32*x) - 2*(16 + 16*x)*sin(2*x))/(128 + 128*x)
sin(2*x) x sin(4*x)
- -------- + - + ---------
4 4 32 + 32*x
$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{32 x + 32}$$
-sin(2*x)/4 + x/4 + sin(4*x)/(32 + 32*x)
2
-8*sin(2*x) + 8*x + 8*x - 8*x*sin(2*x) + sin(4*x)
--------------------------------------------------
32*(1 + x)
$$\frac{8 x^{2} - 8 x \sin{\left(2 x \right)} + 8 x - 8 \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32 \left(x + 1\right)}$$
(-8*sin(2*x) + 8*x + 8*x^2 - 8*x*sin(2*x) + sin(4*x))/(32*(1 + x))
/ -2*I*x 2*I*x\ / -4*I*x 4*I*x\
x I*\- e + e / I*\- e + e /
- + ---------------------- - ----------------------
4 8 4*(16 + 16*x)
$$\frac{x}{4} + \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{8} - \frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{4 \left(16 x + 16\right)}$$
sin(2*x) x sin(4*x)
- -------- + - + -------------
4 4 2*(16 + 16*x)
$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$
-sin(2*x)/4 + x/4 + sin(4*x)/(2*(16 + 16*x))
Abrimos la expresión
[src]
sin(2*x) x sin(4*x)
- -------- + - + ------------
4 4 16*(2 + 2*x)
$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{16 \left(2 x + 2\right)}$$
3
x cos(x)*sin(x) 4*sin (x)*cos(x) 2*cos(x)*sin(x)
- - ------------- - ---------------- + ---------------
4 2 16 + 16*x 16 + 16*x
$$\frac{x}{4} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} - \frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{16 x + 16} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{16 x + 16}$$
x/4 - cos(x)*sin(x)/2 - 4*sin(x)^3*cos(x)/(16 + 16*x) + 2*cos(x)*sin(x)/(16 + 16*x)
Compilar la expresión
[src]
sin(2*x) x sin(4*x)
- -------- + - + -------------
4 4 2*(16 + 16*x)
$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$
-sin(2*x)/4 + x/4 + sin(4*x)/(2*(16 + 16*x))
Parte trigonométrica
[src]
1 x 1
- --------------- + - + ---------------------------
/ pi\ 4 / pi\
4*sec|2*x - --| 2*(16 + 16*x)*sec|4*x - --|
\ 2 / \ 2 /
$$\frac{x}{4} - \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{1}{2 \left(16 x + 16\right) \sec{\left(4 x - \frac{\pi}{2} \right)}}$$
x cot(x) cot(2*x)
- - --------------- + ---------------------------
4 / 2 \ / 2 \
2*\1 + cot (x)/ \1 + cot (2*x)/*(16 + 16*x)
$$\frac{x}{4} - \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)} + \frac{\cot{\left(2 x \right)}}{\left(16 x + 16\right) \left(\cot^{2}{\left(2 x \right)} + 1\right)}$$
1 x 1
- ---------- + - + ----------------------
4*csc(2*x) 4 2*(16 + 16*x)*csc(4*x)
$$\frac{x}{4} - \frac{1}{4 \csc{\left(2 x \right)}} + \frac{1}{2 \left(16 x + 16\right) \csc{\left(4 x \right)}}$$
sin(2*x) x sin(4*x)
- -------- + - + ------------
4 4 16*(2 + 2*x)
$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{16 \left(2 x + 2\right)}$$
x tan(x) tan(2*x)
- - --------------- + ---------------------------
4 / 2 \ / 2 \
2*\1 + tan (x)/ \1 + tan (2*x)/*(16 + 16*x)
$$\frac{x}{4} - \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} + \frac{\tan{\left(2 x \right)}}{\left(16 x + 16\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)}$$
/ pi\ / pi\
cos|2*x - --| cos|4*x - --|
\ 2 / x \ 2 /
- ------------- + - + -------------
4 4 2*(16 + 16*x)
$$\frac{x}{4} - \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} + \frac{\cos{\left(4 x - \frac{\pi}{2} \right)}}{2 \left(16 x + 16\right)}$$
sin(2*x) x sin(4*x)
- -------- + - + -------------
4 4 2*(16 + 16*x)
$$\frac{x}{4} - \frac{\sin{\left(2 x \right)}}{4} + \frac{\sin{\left(4 x \right)}}{2 \left(16 x + 16\right)}$$
-sin(2*x)/4 + x/4 + sin(4*x)/(2*(16 + 16*x))
Unión de expresiones racionales
[src]
-8*(1 + x)*sin(2*x) + 8*x*(1 + x) + sin(4*x)
--------------------------------------------
32*(1 + x)
$$\frac{8 x \left(x + 1\right) - 8 \left(x + 1\right) \sin{\left(2 x \right)} + \sin{\left(4 x \right)}}{32 \left(x + 1\right)}$$
(-8*(1 + x)*sin(2*x) + 8*x*(1 + x) + sin(4*x))/(32*(1 + x))