Simplificación general
[src]
/ x\
sin|2 + -|
sin(6 + x) \ 3/ 1
- ---------- + ---------- - ---------------
8 24 2
(4 + x) *log(2)
$$\frac{\sin{\left(\frac{x}{3} + 2 \right)}}{24} - \frac{\sin{\left(x + 6 \right)}}{8} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}}$$
-sin(6 + x)/8 + sin(2 + x/3)/24 - 1/((4 + x)^2*log(2))
0.166666666666667*sin((x + 6)/3)^3 - 1/((4.0 + x)*(2.77258872223978 + 0.693147180559945*x)) - 0.333333333333333*cos((x + 6)/3)^2*sin((x + 6)/3)
0.166666666666667*sin((x + 6)/3)^3 - 1/((4.0 + x)*(2.77258872223978 + 0.693147180559945*x)) - 0.333333333333333*cos((x + 6)/3)^2*sin((x + 6)/3)
/ 3/ x\ 2 3/ x\ 3/ x\ 2/ x\ / x\ 2 2/ x\ / x\ 2/ x\ / x\\
-|6 - 16*sin |2 + -|*log(2) - x *sin |2 + -|*log(2) - 8*x*sin |2 + -|*log(2) + 32*cos |2 + -|*log(2)*sin|2 + -| + 2*x *cos |2 + -|*log(2)*sin|2 + -| + 16*x*cos |2 + -|*log(2)*sin|2 + -||
\ \ 3/ \ 3/ \ 3/ \ 3/ \ 3/ \ 3/ \ 3/ \ 3/ \ 3//
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
6*(4 + x) *log(2)
$$- \frac{- x^{2} \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} + 2 x^{2} \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} - 8 x \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} + 16 x \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} - 16 \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} + 32 \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} + 6}{6 \left(x + 4\right)^{2} \log{\left(2 \right)}}$$
-(6 - 16*sin(2 + x/3)^3*log(2) - x^2*sin(2 + x/3)^3*log(2) - 8*x*sin(2 + x/3)^3*log(2) + 32*cos(2 + x/3)^2*log(2)*sin(2 + x/3) + 2*x^2*cos(2 + x/3)^2*log(2)*sin(2 + x/3) + 16*x*cos(2 + x/3)^2*log(2)*sin(2 + x/3))/(6*(4 + x)^2*log(2))
Unión de expresiones racionales
[src]
2 3/ x\ 2 2/ x\ / x\
-6 + (4 + x) *sin |2 + -|*log(2) - 2*(4 + x) *cos |2 + -|*log(2)*sin|2 + -|
\ 3/ \ 3/ \ 3/
---------------------------------------------------------------------------
2
6*(4 + x) *log(2)
$$\frac{\left(x + 4\right)^{2} \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} - 2 \left(x + 4\right)^{2} \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} - 6}{6 \left(x + 4\right)^{2} \log{\left(2 \right)}}$$
(-6 + (4 + x)^2*sin(2 + x/3)^3*log(2) - 2*(4 + x)^2*cos(2 + x/3)^2*log(2)*sin(2 + x/3))/(6*(4 + x)^2*log(2))
Abrimos la expresión
[src]
3/x + 6\ 2/x + 6\ /x + 6\
sin |-----| cos |-----|*sin|-----|
\ 3 / 1 \ 3 / \ 3 /
----------- - --------------- - ----------------------
6 2 3
(x + 4) *log(2)
$$- \frac{\sin{\left(\frac{x + 6}{3} \right)} \cos^{2}{\left(\frac{x + 6}{3} \right)}}{3} + \frac{\sin^{3}{\left(\frac{x + 6}{3} \right)}}{6} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}}$$
3/x\ 2/x\ /x\ 6 3/x\ 4 2 3/x\ 5 3/x\ 6 2/x\ /x\ 3/x\ 2 2 3/x\ 3 3/x\ 3 3 3/x\ 3 2/x\ /x\ 2 2/x\ 2 /x\ 3 3 2/x\ /x\ 2/x\ /x\ 4 2/x\ 2 /x\ 5 2/x\ /x\
sin |-| cos |-|*sin|-| 4*cos (1)*sin |-| 8*cos (1)*sin (1)*sin |-| 8*cos (1)*cos |-|*sin(1) 8*cos (1)*cos |-|*sin|-| 2*cos |-|*cos(1)*sin(1) 4*cos (1)*sin (1)*sin |-| 4*cos (1)*cos |-|*sin (1) 8*cos (1)*cos |-|*sin(1) 28*cos (1)*sin |-|*cos|-|*sin(1) 14*cos (1)*cos |-|*sin (1)*sin|-| 8*cos (1)*sin (1)*sin |-|*cos|-| 7*sin |-|*cos(1)*cos|-|*sin(1) 28*cos (1)*cos |-|*sin (1)*sin|-| 28*cos (1)*sin |-|*cos|-|*sin(1)
1 \3/ 2 3/x\ 4 3/x\ \3/ \3/ \3/ 2 2/x\ /x\ 4 2/x\ /x\ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/ \3/
- ---------------------------------- - ------- + cos (1)*sin |-| - 2*cos (1)*sin |-| + -------------- + ----------------- - 2*cos (1)*cos |-|*sin|-| + 4*cos (1)*cos |-|*sin|-| - ------------------------- - ------------------------ - ------------------------ - ----------------------- + ------------------------- + ------------------------- + ------------------------ - -------------------------------- - --------------------------------- - -------------------------------- + ------------------------------ + --------------------------------- + --------------------------------
2 6 \3/ \3/ 3 3 \3/ \3/ \3/ \3/ 3 3 3 3 3 3 3 3 3 3 3 3 3
16*log(2) + x *log(2) + 8*x*log(2)
$$- 2 \sin^{3}{\left(\frac{x}{3} \right)} \cos^{4}{\left(1 \right)} - \frac{\sin^{3}{\left(\frac{x}{3} \right)}}{6} - \frac{8 \sin^{2}{\left(1 \right)} \sin^{3}{\left(\frac{x}{3} \right)} \cos^{4}{\left(1 \right)}}{3} + \frac{4 \sin^{3}{\left(\frac{x}{3} \right)} \cos^{6}{\left(1 \right)}}{3} + \frac{4 \sin^{2}{\left(1 \right)} \sin^{3}{\left(\frac{x}{3} \right)} \cos^{2}{\left(1 \right)}}{3} + \sin^{3}{\left(\frac{x}{3} \right)} \cos^{2}{\left(1 \right)} - \frac{28 \sin{\left(1 \right)} \sin^{2}{\left(\frac{x}{3} \right)} \cos^{3}{\left(1 \right)} \cos{\left(\frac{x}{3} \right)}}{3} - \frac{8 \sin^{3}{\left(1 \right)} \sin^{2}{\left(\frac{x}{3} \right)} \cos^{3}{\left(1 \right)} \cos{\left(\frac{x}{3} \right)}}{3} + \frac{28 \sin{\left(1 \right)} \sin^{2}{\left(\frac{x}{3} \right)} \cos^{5}{\left(1 \right)} \cos{\left(\frac{x}{3} \right)}}{3} + \frac{7 \sin{\left(1 \right)} \sin^{2}{\left(\frac{x}{3} \right)} \cos{\left(1 \right)} \cos{\left(\frac{x}{3} \right)}}{3} - \frac{14 \sin^{2}{\left(1 \right)} \sin{\left(\frac{x}{3} \right)} \cos^{2}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{3} - 2 \sin{\left(\frac{x}{3} \right)} \cos^{2}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)} - \frac{8 \sin{\left(\frac{x}{3} \right)} \cos^{6}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{3} + \frac{\sin{\left(\frac{x}{3} \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{3} + 4 \sin{\left(\frac{x}{3} \right)} \cos^{4}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)} + \frac{28 \sin^{2}{\left(1 \right)} \sin{\left(\frac{x}{3} \right)} \cos^{4}{\left(1 \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{3} - \frac{2 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos^{3}{\left(\frac{x}{3} \right)}}{3} - \frac{8 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)} \cos^{3}{\left(\frac{x}{3} \right)}}{3} + \frac{4 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos^{3}{\left(\frac{x}{3} \right)}}{3} + \frac{8 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)} \cos^{3}{\left(\frac{x}{3} \right)}}{3} - \frac{1}{x^{2} \log{\left(2 \right)} + 8 x \log{\left(2 \right)} + 16 \log{\left(2 \right)}}$$
-1/(16*log(2) + x^2*log(2) + 8*x*log(2)) - sin(x/3)^3/6 + cos(1)^2*sin(x/3)^3 - 2*cos(1)^4*sin(x/3)^3 + cos(x/3)^2*sin(x/3)/3 + 4*cos(1)^6*sin(x/3)^3/3 - 2*cos(1)^2*cos(x/3)^2*sin(x/3) + 4*cos(1)^4*cos(x/3)^2*sin(x/3) - 8*cos(1)^4*sin(1)^2*sin(x/3)^3/3 - 8*cos(1)^5*cos(x/3)^3*sin(1)/3 - 8*cos(1)^6*cos(x/3)^2*sin(x/3)/3 - 2*cos(x/3)^3*cos(1)*sin(1)/3 + 4*cos(1)^2*sin(1)^2*sin(x/3)^3/3 + 4*cos(1)^3*cos(x/3)^3*sin(1)^3/3 + 8*cos(1)^3*cos(x/3)^3*sin(1)/3 - 28*cos(1)^3*sin(x/3)^2*cos(x/3)*sin(1)/3 - 14*cos(1)^2*cos(x/3)^2*sin(1)^2*sin(x/3)/3 - 8*cos(1)^3*sin(1)^3*sin(x/3)^2*cos(x/3)/3 + 7*sin(x/3)^2*cos(1)*cos(x/3)*sin(1)/3 + 28*cos(1)^4*cos(x/3)^2*sin(1)^2*sin(x/3)/3 + 28*cos(1)^5*sin(x/3)^2*cos(x/3)*sin(1)/3
Compilar la expresión
[src]
3/x + 6\ 2/x + 6\ /x + 6\
sin |-----| cos |-----|*sin|-----|
\ 3 / 1 \ 3 / \ 3 /
----------- - --------------- - ----------------------
6 2 3
(4 + x) *log(2)
$$\frac{\sin^{3}{\left(\frac{x + 6}{3} \right)}}{6} - \frac{\sin{\left(\frac{x + 6}{3} \right)} \cos^{2}{\left(\frac{x + 6}{3} \right)}}{3} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}}$$
sin((x + 6)/3)^3/6 - 1/((4 + x)^2*log(2)) - cos((x + 6)/3)^2*sin((x + 6)/3)/3
3/ x\ 2/ x\ / x\
sin |2 + -| cos |2 + -|*sin|2 + -|
1 \ 3/ \ 3/ \ 3/
- ---------------------------------- + ----------- - ----------------------
2 6 3
16*log(2) + x *log(2) + 8*x*log(2)
$$\frac{\sin^{3}{\left(\frac{x}{3} + 2 \right)}}{6} - \frac{\sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)}}{3} - \frac{1}{x^{2} \log{\left(2 \right)} + 8 x \log{\left(2 \right)} + 16 \log{\left(2 \right)}}$$
-1/(16*log(2) + x^2*log(2) + 8*x*log(2)) + sin(2 + x/3)^3/6 - cos(2 + x/3)^2*sin(2 + x/3)/3
2
/ / x\ / x\\
3 | I*|-2 - -| I*|2 + -|| / / x\ / x\\
/ / x\ / x\\ | \ 3/ \ 3/| | I*|-2 - -| I*|2 + -||
| I*|-2 - -| I*|2 + -|| |e e | | \ 3/ \ 3/|
| \ 3/ \ 3/| I*|----------- + ----------| *\- e + e /
1 I*\- e + e / \ 2 2 /
- --------------- + ------------------------------- + ----------------------------------------------------------
2 48 6
(4 + x) *log(2)
$$\frac{i \left(- e^{i \left(- \frac{x}{3} - 2\right)} + e^{i \left(\frac{x}{3} + 2\right)}\right)^{3}}{48} + \frac{i \left(- e^{i \left(- \frac{x}{3} - 2\right)} + e^{i \left(\frac{x}{3} + 2\right)}\right) \left(\frac{e^{i \left(- \frac{x}{3} - 2\right)}}{2} + \frac{e^{i \left(\frac{x}{3} + 2\right)}}{2}\right)^{2}}{6} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}}$$
3/ x\ 2/ x\ / x\
sin |2 + -| cos |2 + -|*sin|2 + -|
\ 3/ 1 \ 3/ \ 3/
----------- - --------------- - ----------------------
6 2 3
(4 + x) *log(2)
$$\frac{\sin^{3}{\left(\frac{x}{3} + 2 \right)}}{6} - \frac{\sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)}}{3} - \frac{1}{\left(x + 4\right)^{2} \log{\left(2 \right)}}$$
sin(2 + x/3)^3/6 - 1/((4 + x)^2*log(2)) - cos(2 + x/3)^2*sin(2 + x/3)/3
Denominador racional
[src]
2 3/ x\ 2 2/ x\ / x\
-18 + 3*(4 + x) *sin |2 + -|*log(2) - 6*(4 + x) *cos |2 + -|*log(2)*sin|2 + -|
\ 3/ \ 3/ \ 3/
------------------------------------------------------------------------------
2
18*(4 + x) *log(2)
$$\frac{3 \left(x + 4\right)^{2} \log{\left(2 \right)} \sin^{3}{\left(\frac{x}{3} + 2 \right)} - 6 \left(x + 4\right)^{2} \log{\left(2 \right)} \sin{\left(\frac{x}{3} + 2 \right)} \cos^{2}{\left(\frac{x}{3} + 2 \right)} - 18}{18 \left(x + 4\right)^{2} \log{\left(2 \right)}}$$
(-18 + 3*(4 + x)^2*sin(2 + x/3)^3*log(2) - 6*(4 + x)^2*cos(2 + x/3)^2*log(2)*sin(2 + x/3))/(18*(4 + x)^2*log(2))