Simplificación general
[src]
3 2
/ 2\ / /x \\ / 2\ / 2\ 2
\1 + 100*x / *|-10412307*atan(10*x)*cos(27*x) + sin|--|| + \-1058000 - 105800000*x /*(81*x*cos(27*x) + sin(27*x)) - 11569230*\1 + 100*x / *sin(27*x) + 423200000*x *sin(27*x)
\ \23//
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
/ 2\
529*\1 + 100*x /
$$\frac{423200000 x^{2} \sin{\left(27 x \right)} + \left(- 105800000 x^{2} - 1058000\right) \left(81 x \cos{\left(27 x \right)} + \sin{\left(27 x \right)}\right) + \left(100 x^{2} + 1\right)^{3} \left(\sin{\left(\frac{x}{23} \right)} - 10412307 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)}\right) - 11569230 \left(100 x^{2} + 1\right)^{2} \sin{\left(27 x \right)}}{529 \left(100 x^{2} + 1\right)^{3}}$$
((1 + 100*x^2)^3*(-10412307*atan(10*x)*cos(27*x) + sin(x/23)) + (-1058000 - 105800000*x^2)*(81*x*cos(27*x) + sin(27*x)) - 11569230*(1 + 100*x^2)^2*sin(27*x) + 423200000*x^2*sin(27*x))/(529*(1 + 100*x^2)^3)
Denominador racional
[src]
3 / 2 / 2 \ 2 \ 4
/ 2\ |/ 2\ |/ 2\ / / 2\ /x \ / 2\ \ / 2\ | / 2\ / 2\ | 2 / 2\ / 2\
\1 + 100*x / *|\1 + 100*x / *|\1 + 100*x / *|-11569230*sin(27*x) + \1 + 100*x /*sin|--| - 19683*\529 + 52900*x /*atan(10*x)*cos(27*x)| - 2000*\529 + 52900*x /*sin(27*x)| - 162000*x*\1 + 100*x / *\529 + 52900*x /*cos(27*x)| + 800000*x *\1 + 100*x / *\529 + 52900*x /*sin(27*x)
\ \ \ \23/ / / /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
7
/ 2\ / 2\
\1 + 100*x / *\529 + 52900*x /
$$\frac{800000 x^{2} \left(100 x^{2} + 1\right)^{4} \left(52900 x^{2} + 529\right) \sin{\left(27 x \right)} + \left(100 x^{2} + 1\right)^{3} \left(- 162000 x \left(100 x^{2} + 1\right)^{2} \left(52900 x^{2} + 529\right) \cos{\left(27 x \right)} + \left(100 x^{2} + 1\right)^{2} \left(\left(100 x^{2} + 1\right)^{2} \left(\left(100 x^{2} + 1\right) \sin{\left(\frac{x}{23} \right)} - 19683 \left(52900 x^{2} + 529\right) \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - 11569230 \sin{\left(27 x \right)}\right) - 2000 \left(52900 x^{2} + 529\right) \sin{\left(27 x \right)}\right)\right)}{\left(100 x^{2} + 1\right)^{7} \left(52900 x^{2} + 529\right)}$$
((1 + 100*x^2)^3*((1 + 100*x^2)^2*((1 + 100*x^2)^2*(-11569230*sin(27*x) + (1 + 100*x^2)*sin(x/23) - 19683*(529 + 52900*x^2)*atan(10*x)*cos(27*x)) - 2000*(529 + 52900*x^2)*sin(27*x)) - 162000*x*(1 + 100*x^2)^2*(529 + 52900*x^2)*cos(27*x)) + 800000*x^2*(1 + 100*x^2)^4*(529 + 52900*x^2)*sin(27*x))/((1 + 100*x^2)^7*(529 + 52900*x^2))
/ -I*x I*x\ / -27*I*x 27*I*x\
| ----- ---| |e e |
/ -27*I*x 27*I*x\ | 23 23| 162000*x*|-------- + -------| / -27*I*x 27*I*x\ / -27*I*x 27*I*x\ 2 / -27*I*x 27*I*x\
|e e | I*\- e + e / \ 2 2 / 1000*I*\- e + e / 10935*I*\- e + e / 400000*I*x *\- e + e /
- 19683*|-------- + -------|*atan(10*x) - ------------------- - ----------------------------- + ----------------------------- + ------------------------------ - ----------------------------------
\ 2 2 / 1058 2 2 2 3
/ 2\ / 2\ 1 + 100*x / 2\
\1 + 100*x / \1 + 100*x / \1 + 100*x /
$$- \frac{400000 i x^{2} \left(e^{27 i x} - e^{- 27 i x}\right)}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \left(\frac{e^{27 i x}}{2} + \frac{e^{- 27 i x}}{2}\right)}{\left(100 x^{2} + 1\right)^{2}} - \frac{i \left(e^{\frac{i x}{23}} - e^{- \frac{i x}{23}}\right)}{1058} - 19683 \left(\frac{e^{27 i x}}{2} + \frac{e^{- 27 i x}}{2}\right) \operatorname{atan}{\left(10 x \right)} + \frac{10935 i \left(e^{27 i x} - e^{- 27 i x}\right)}{100 x^{2} + 1} + \frac{1000 i \left(e^{27 i x} - e^{- 27 i x}\right)}{\left(100 x^{2} + 1\right)^{2}}$$
/x \
sin|--| 2
\23/ 21870*sin(27*x) 2000*sin(27*x) 162000*x*cos(27*x) 800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*cos(27*x) - -------------- - ------------------ + -------------------
529 2 2 2 3
1 + 100*x / 2\ / 2\ / 2\
\1 + 100*x / \1 + 100*x / \1 + 100*x /
$$\frac{800000 x^{2} \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \cos{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{x}{23} \right)}}{529} - 19683 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - \frac{21870 \sin{\left(27 x \right)}}{100 x^{2} + 1} - \frac{2000 \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}}$$
sin(x/23)/529 - 21870*sin(27*x)/(1 + 100*x^2) - 19683*atan(10*x)*cos(27*x) - 2000*sin(27*x)/(1 + 100*x^2)^2 - 162000*x*cos(27*x)/(1 + 100*x^2)^2 + 800000*x^2*sin(27*x)/(1 + 100*x^2)^3
/ /x \ 6 /x \ 4 /x \ 2 /x \ 2 3 4 2 4 6 \
-|- sin|--| + 12627230*sin(27*x) - 1000000*x *sin|--| - 30000*x *sin|--| - 300*x *sin|--| + 10412307*atan(10*x)*cos(27*x) + 85698000*x*cos(27*x) + 1996446000*x *sin(27*x) + 8569800000*x *cos(27*x) + 115692300000*x *sin(27*x) + 3123692100*x *atan(10*x)*cos(27*x) + 312369210000*x *atan(10*x)*cos(27*x) + 10412307000000*x *atan(10*x)*cos(27*x)|
\ \23/ \23/ \23/ \23/ /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
/ 2\
529*\1 + 100*x /
$$- \frac{- 1000000 x^{6} \sin{\left(\frac{x}{23} \right)} + 10412307000000 x^{6} \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - 30000 x^{4} \sin{\left(\frac{x}{23} \right)} + 115692300000 x^{4} \sin{\left(27 x \right)} + 312369210000 x^{4} \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} + 8569800000 x^{3} \cos{\left(27 x \right)} - 300 x^{2} \sin{\left(\frac{x}{23} \right)} + 1996446000 x^{2} \sin{\left(27 x \right)} + 3123692100 x^{2} \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} + 85698000 x \cos{\left(27 x \right)} - \sin{\left(\frac{x}{23} \right)} + 12627230 \sin{\left(27 x \right)} + 10412307 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)}}{529 \left(100 x^{2} + 1\right)^{3}}$$
-(-sin(x/23) + 12627230*sin(27*x) - 1000000*x^6*sin(x/23) - 30000*x^4*sin(x/23) - 300*x^2*sin(x/23) + 10412307*atan(10*x)*cos(27*x) + 85698000*x*cos(27*x) + 1996446000*x^2*sin(27*x) + 8569800000*x^3*cos(27*x) + 115692300000*x^4*sin(27*x) + 3123692100*x^2*atan(10*x)*cos(27*x) + 312369210000*x^4*atan(10*x)*cos(27*x) + 10412307000000*x^6*atan(10*x)*cos(27*x))/(529*(1 + 100*x^2)^3)
Compilar la expresión
[src]
/x \
sin|--| 2
\23/ 21870*sin(27*x) 2000*sin(27*x) 162000*x*cos(27*x) 800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*cos(27*x) - -------------- - ------------------ + -------------------
529 2 2 2 3
1 + 100*x / 2\ / 2\ / 2\
\1 + 100*x / \1 + 100*x / \1 + 100*x /
$$\frac{800000 x^{2} \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \cos{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{x}{23} \right)}}{529} - 19683 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - \frac{21870 \sin{\left(27 x \right)}}{100 x^{2} + 1} - \frac{2000 \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}}$$
sin(x/23)/529 - 21870*sin(27*x)/(1 + 100*x^2) - 19683*atan(10*x)*cos(27*x) - 2000*sin(27*x)/(1 + 100*x^2)^2 - 162000*x*cos(27*x)/(1 + 100*x^2)^2 + 800000*x^2*sin(27*x)/(1 + 100*x^2)^3
Abrimos la expresión
[src]
/x \
sin|--| 21 17 25 13 21 17 25 13 9 9 5 5 3 3 7 7 27 11 27 15 11 23 19 15 23 19 2 19 2 23 2 15 19 23 15 2 11 2 27 11 27 2 7 7 2 3 3 2 5 2 5 9 2 9 13 25 2 13 17 2 25 21 2 17 2 21
\23/ 19 52216977162240*sin (x) 46321928110080*sin (x) 23 15 9906778275840*sin (x) 9374675927040*sin (x) 4775215104000*sin (x) 4236115968000*sin (x) 11 27 905969664000*sin (x) 857309184000*sin (x) 408314649600*sin (x) 7 37340160000*sin (x) 2579260320*sin (x) 235872000*sin (x) 3 590490*sin(x) 54000*sin(x) 6552000*sin (x) 71646120*sin (x) 5 3953664000*sin (x) 43233315840*sin (x) 134217728000*sin (x) 219967488000*sin (x) 9 1467670855680*sin (x) 2286157824000*sin (x) 2405344481280*sin (x) 2717908992000*sin (x) 5449973760000*sin (x) 13 25 24999135805440*sin (x) 29720334827520*sin (x) 17 21 59595463065600*sin (x) 2179989504000000*x *sin (x) 1087163596800000*x *sin (x) 914463129600000*x *sin (x) 441447874560000*x*cos (x) 220150628352000*x*cos (x) 185178783744000*x*cos (x) 87986995200000*x *sin (x) 53687091200000*x *sin (x) 17817366528000*x*cos (x) 10871635968000*x*cos (x) 1581465600000*x *sin (x) 320246784000*x*cos (x) 2620800000*x *sin (x) 530712000*x*cos (x) 4374000*x*cos(x) 21600000*x *sin(x) 19105632000*x*cos (x) 94348800000*x *sin (x) 3024552960000*x*cos (x) 14936064000000*x *sin (x) 69442043904000*x*cos (x) 73383542784000*x*cos (x) 342923673600000*x *sin (x) 343125393408000*x*cos (x) 362387865600000*x *sin (x) 386792423424000*x*cos (x) 1694446387200000*x *sin (x) 1910086041600000*x *sin (x)
------- - 53635916759040*cos (x)*atan(10*x) - ----------------------- - ----------------------- - 26748301344768*cos (x)*atan(10*x) - 22499222224896*cos (x)*atan(10*x) - ---------------------- - ---------------------- - ---------------------- - ---------------------- - 2164810033152*cos (x)*atan(10*x) - 1320903770112*cos (x)*atan(10*x) - --------------------- - --------------------- - -------------------- - 38909984256*cos (x)*atan(10*x) - --------------------- - ------------------ - --------------------- - 64481508*cos (x)*atan(10*x) - ------------- - --------------------- + 531441*atan(10*x)*cos(x) + --------------------- + ---------------- + 2321334288*cos (x)*atan(10*x) + --------------------- + ------------------- + --------------------- + --------------------- + 367483184640*cos (x)*atan(10*x) + ---------------------- + ---------------------- + ---------------------- + ---------------------- + ---------------------- + 8437208334336*cos (x)*atan(10*x) + 8916100448256*cos (x)*atan(10*x) + ----------------------- + ----------------------- + 41689735299072*cos (x)*atan(10*x) + 46995279446016*cos (x)*atan(10*x) + ----------------------- - ---------------------------------- - ---------------------------------- - ---------------------------------- - -------------------------- - -------------------------- - -------------------------- - ---------------------------------- - ---------------------------------- - ------------------------- - ------------------------- - ---------------------------------- - ---------------------- - ---------------------------------- - --------------------- + --------------------- + ---------------------------------- + --------------------- + ---------------------------------- + ----------------------- + ---------------------------------- + ------------------------- + ------------------------- + ---------------------------------- + -------------------------- + ---------------------------------- + -------------------------- + ---------------------------------- + ----------------------------------
529 2 2 2 2 2 4 2 4 2 4 2 4 2 2 4 2 2 4 2 2 4 2 4 2 2 4 2 2 4 2 4 2 2 4 2 2 4 2 4 2 2 2 2 4 6 2 4 6 2 4 6 2 4 2 4 2 4 2 4 6 2 4 6 2 4 2 4 2 4 6 2 4 2 4 6 2 4 2 4 2 4 6 2 4 2 4 6 2 4 2 4 6 2 4 2 4 2 4 6 2 4 2 4 6 2 4 2 4 6 2 4 6
1 + 100*x 1 + 100*x 1 + 100*x 1 + 100*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 100*x 1 + 200*x + 10000*x 1 + 100*x 1 + 200*x + 10000*x 1 + 100*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 100*x 1 + 200*x + 10000*x 1 + 100*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 100*x 1 + 200*x + 10000*x 1 + 100*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 100*x 1 + 100*x 1 + 100*x 1 + 300*x + 30000*x + 1000000*x 1 + 300*x + 30000*x + 1000000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 200*x + 10000*x 1 + 300*x + 30000*x + 1000000*x 1 + 300*x + 30000*x + 1000000*x
$$- \frac{53687091200000 x^{2} \sin^{27}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{362387865600000 x^{2} \sin^{25}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{1087163596800000 x^{2} \sin^{23}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{1910086041600000 x^{2} \sin^{21}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{2179989504000000 x^{2} \sin^{19}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{1694446387200000 x^{2} \sin^{17}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{914463129600000 x^{2} \sin^{15}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{342923673600000 x^{2} \sin^{13}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{87986995200000 x^{2} \sin^{11}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{14936064000000 x^{2} \sin^{9}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{1581465600000 x^{2} \sin^{7}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{94348800000 x^{2} \sin^{5}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{2620800000 x^{2} \sin^{3}{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} + \frac{21600000 x^{2} \sin{\left(x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1} - \frac{10871635968000 x \cos^{27}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{73383542784000 x \cos^{25}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{220150628352000 x \cos^{23}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{386792423424000 x \cos^{21}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{441447874560000 x \cos^{19}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{343125393408000 x \cos^{17}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{185178783744000 x \cos^{15}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{69442043904000 x \cos^{13}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{17817366528000 x \cos^{11}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{3024552960000 x \cos^{9}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{320246784000 x \cos^{7}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{19105632000 x \cos^{5}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{530712000 x \cos^{3}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{4374000 x \cos{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{\sin{\left(\frac{x}{23} \right)}}{529} - 1320903770112 \cos^{27}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 8916100448256 \cos^{25}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 26748301344768 \cos^{23}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 46995279446016 \cos^{21}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 53635916759040 \cos^{19}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 41689735299072 \cos^{17}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 22499222224896 \cos^{15}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 8437208334336 \cos^{13}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 2164810033152 \cos^{11}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 367483184640 \cos^{9}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 38909984256 \cos^{7}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 2321334288 \cos^{5}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} - 64481508 \cos^{3}{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + 531441 \cos{\left(x \right)} \operatorname{atan}{\left(10 x \right)} + \frac{134217728000 \sin^{27}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{905969664000 \sin^{25}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{2717908992000 \sin^{23}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{4775215104000 \sin^{21}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{5449973760000 \sin^{19}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{4236115968000 \sin^{17}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{2286157824000 \sin^{15}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{857309184000 \sin^{13}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{219967488000 \sin^{11}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{37340160000 \sin^{9}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{3953664000 \sin^{7}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{235872000 \sin^{5}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{6552000 \sin^{3}{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} - \frac{54000 \sin{\left(x \right)}}{10000 x^{4} + 200 x^{2} + 1} + \frac{1467670855680 \sin^{27}{\left(x \right)}}{100 x^{2} + 1} - \frac{9906778275840 \sin^{25}{\left(x \right)}}{100 x^{2} + 1} + \frac{29720334827520 \sin^{23}{\left(x \right)}}{100 x^{2} + 1} - \frac{52216977162240 \sin^{21}{\left(x \right)}}{100 x^{2} + 1} + \frac{59595463065600 \sin^{19}{\left(x \right)}}{100 x^{2} + 1} - \frac{46321928110080 \sin^{17}{\left(x \right)}}{100 x^{2} + 1} + \frac{24999135805440 \sin^{15}{\left(x \right)}}{100 x^{2} + 1} - \frac{9374675927040 \sin^{13}{\left(x \right)}}{100 x^{2} + 1} + \frac{2405344481280 \sin^{11}{\left(x \right)}}{100 x^{2} + 1} - \frac{408314649600 \sin^{9}{\left(x \right)}}{100 x^{2} + 1} + \frac{43233315840 \sin^{7}{\left(x \right)}}{100 x^{2} + 1} - \frac{2579260320 \sin^{5}{\left(x \right)}}{100 x^{2} + 1} + \frac{71646120 \sin^{3}{\left(x \right)}}{100 x^{2} + 1} - \frac{590490 \sin{\left(x \right)}}{100 x^{2} + 1}$$
sin(x/23)/529 - 53635916759040*cos(x)^19*atan(10*x) - 52216977162240*sin(x)^21/(1 + 100*x^2) - 46321928110080*sin(x)^17/(1 + 100*x^2) - 26748301344768*cos(x)^23*atan(10*x) - 22499222224896*cos(x)^15*atan(10*x) - 9906778275840*sin(x)^25/(1 + 100*x^2) - 9374675927040*sin(x)^13/(1 + 100*x^2) - 4775215104000*sin(x)^21/(1 + 200*x^2 + 10000*x^4) - 4236115968000*sin(x)^17/(1 + 200*x^2 + 10000*x^4) - 2164810033152*cos(x)^11*atan(10*x) - 1320903770112*cos(x)^27*atan(10*x) - 905969664000*sin(x)^25/(1 + 200*x^2 + 10000*x^4) - 857309184000*sin(x)^13/(1 + 200*x^2 + 10000*x^4) - 408314649600*sin(x)^9/(1 + 100*x^2) - 38909984256*cos(x)^7*atan(10*x) - 37340160000*sin(x)^9/(1 + 200*x^2 + 10000*x^4) - 2579260320*sin(x)^5/(1 + 100*x^2) - 235872000*sin(x)^5/(1 + 200*x^2 + 10000*x^4) - 64481508*cos(x)^3*atan(10*x) - 590490*sin(x)/(1 + 100*x^2) - 54000*sin(x)/(1 + 200*x^2 + 10000*x^4) + 531441*atan(10*x)*cos(x) + 6552000*sin(x)^3/(1 + 200*x^2 + 10000*x^4) + 71646120*sin(x)^3/(1 + 100*x^2) + 2321334288*cos(x)^5*atan(10*x) + 3953664000*sin(x)^7/(1 + 200*x^2 + 10000*x^4) + 43233315840*sin(x)^7/(1 + 100*x^2) + 134217728000*sin(x)^27/(1 + 200*x^2 + 10000*x^4) + 219967488000*sin(x)^11/(1 + 200*x^2 + 10000*x^4) + 367483184640*cos(x)^9*atan(10*x) + 1467670855680*sin(x)^27/(1 + 100*x^2) + 2286157824000*sin(x)^15/(1 + 200*x^2 + 10000*x^4) + 2405344481280*sin(x)^11/(1 + 100*x^2) + 2717908992000*sin(x)^23/(1 + 200*x^2 + 10000*x^4) + 5449973760000*sin(x)^19/(1 + 200*x^2 + 10000*x^4) + 8437208334336*cos(x)^13*atan(10*x) + 8916100448256*cos(x)^25*atan(10*x) + 24999135805440*sin(x)^15/(1 + 100*x^2) + 29720334827520*sin(x)^23/(1 + 100*x^2) + 41689735299072*cos(x)^17*atan(10*x) + 46995279446016*cos(x)^21*atan(10*x) + 59595463065600*sin(x)^19/(1 + 100*x^2) - 2179989504000000*x^2*sin(x)^19/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 1087163596800000*x^2*sin(x)^23/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 914463129600000*x^2*sin(x)^15/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 441447874560000*x*cos(x)^19/(1 + 200*x^2 + 10000*x^4) - 220150628352000*x*cos(x)^23/(1 + 200*x^2 + 10000*x^4) - 185178783744000*x*cos(x)^15/(1 + 200*x^2 + 10000*x^4) - 87986995200000*x^2*sin(x)^11/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 53687091200000*x^2*sin(x)^27/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 17817366528000*x*cos(x)^11/(1 + 200*x^2 + 10000*x^4) - 10871635968000*x*cos(x)^27/(1 + 200*x^2 + 10000*x^4) - 1581465600000*x^2*sin(x)^7/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 320246784000*x*cos(x)^7/(1 + 200*x^2 + 10000*x^4) - 2620800000*x^2*sin(x)^3/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 530712000*x*cos(x)^3/(1 + 200*x^2 + 10000*x^4) + 4374000*x*cos(x)/(1 + 200*x^2 + 10000*x^4) + 21600000*x^2*sin(x)/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 19105632000*x*cos(x)^5/(1 + 200*x^2 + 10000*x^4) + 94348800000*x^2*sin(x)^5/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 3024552960000*x*cos(x)^9/(1 + 200*x^2 + 10000*x^4) + 14936064000000*x^2*sin(x)^9/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 69442043904000*x*cos(x)^13/(1 + 200*x^2 + 10000*x^4) + 73383542784000*x*cos(x)^25/(1 + 200*x^2 + 10000*x^4) + 342923673600000*x^2*sin(x)^13/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 343125393408000*x*cos(x)^17/(1 + 200*x^2 + 10000*x^4) + 362387865600000*x^2*sin(x)^25/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 386792423424000*x*cos(x)^21/(1 + 200*x^2 + 10000*x^4) + 1694446387200000*x^2*sin(x)^17/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) + 1910086041600000*x^2*sin(x)^21/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6)
/x \
sin|--| 2 3 4
\23/ 23870*sin(27*x) + 162000*x*cos(27*x) + 3774000*x *sin(27*x) + 16200000*x *cos(27*x) + 218700000*x *sin(27*x)
------- - ------------------------------------------------------------------------------------------------------------ - 19683*atan(10*x)*cos(27*x)
529 2 4 6
1 + 300*x + 30000*x + 1000000*x
$$\frac{\sin{\left(\frac{x}{23} \right)}}{529} - 19683 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - \frac{218700000 x^{4} \sin{\left(27 x \right)} + 16200000 x^{3} \cos{\left(27 x \right)} + 3774000 x^{2} \sin{\left(27 x \right)} + 162000 x \cos{\left(27 x \right)} + 23870 \sin{\left(27 x \right)}}{1000000 x^{6} + 30000 x^{4} + 300 x^{2} + 1}$$
sin(x/23)/529 - (23870*sin(27*x) + 162000*x*cos(27*x) + 3774000*x^2*sin(27*x) + 16200000*x^3*cos(27*x) + 218700000*x^4*sin(27*x))/(1 + 300*x^2 + 30000*x^4 + 1000000*x^6) - 19683*atan(10*x)*cos(27*x)
Unión de expresiones racionales
[src]
/ 2\ / / 2\ / / 2\ /x \ / 2\ \ \ 2
\1 + 100*x /*|-1058000*sin(27*x) + \1 + 100*x /*|-11569230*sin(27*x) + \1 + 100*x /*sin|--| - 10412307*\1 + 100*x /*atan(10*x)*cos(27*x)| - 85698000*x*cos(27*x)| + 423200000*x *sin(27*x)
\ \ \23/ / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
/ 2\
529*\1 + 100*x /
$$\frac{423200000 x^{2} \sin{\left(27 x \right)} + \left(100 x^{2} + 1\right) \left(- 85698000 x \cos{\left(27 x \right)} + \left(100 x^{2} + 1\right) \left(\left(100 x^{2} + 1\right) \sin{\left(\frac{x}{23} \right)} - 10412307 \left(100 x^{2} + 1\right) \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - 11569230 \sin{\left(27 x \right)}\right) - 1058000 \sin{\left(27 x \right)}\right)}{529 \left(100 x^{2} + 1\right)^{3}}$$
((1 + 100*x^2)*(-1058000*sin(27*x) + (1 + 100*x^2)*(-11569230*sin(27*x) + (1 + 100*x^2)*sin(x/23) - 10412307*(1 + 100*x^2)*atan(10*x)*cos(27*x)) - 85698000*x*cos(27*x)) + 423200000*x^2*sin(27*x))/(529*(1 + 100*x^2)^3)
Parte trigonométrica
[src]
/x \ /27*x\ / 2/27*x\\ /27*x\ / 2/27*x\\ 2 /27*x\
2*cot|--| 43740*cot|----| 19683*|-1 + cot |----||*atan(10*x) 4000*cot|----| 162000*x*|-1 + cot |----|| 1600000*x *cot|----|
\46/ \ 2 / \ \ 2 // \ 2 / \ \ 2 // \ 2 /
------------------ - ----------------------------- - ---------------------------------- - ------------------------------ - ------------------------------ + ------------------------------
/ 2/x \\ / 2/27*x\\ / 2\ 2/27*x\ 2 2 3
529*|1 + cot |--|| |1 + cot |----||*\1 + 100*x / 1 + cot |----| / 2/27*x\\ / 2\ / 2/27*x\\ / 2\ / 2/27*x\\ / 2\
\ \46// \ \ 2 // \ 2 / |1 + cot |----||*\1 + 100*x / |1 + cot |----||*\1 + 100*x / |1 + cot |----||*\1 + 100*x /
\ \ 2 // \ \ 2 // \ \ 2 //
$$\frac{1600000 x^{2} \cot{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right)^{3} \left(\cot^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{162000 x \left(\cot^{2}{\left(\frac{27 x}{2} \right)} - 1\right)}{\left(100 x^{2} + 1\right)^{2} \left(\cot^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{19683 \left(\cot^{2}{\left(\frac{27 x}{2} \right)} - 1\right) \operatorname{atan}{\left(10 x \right)}}{\cot^{2}{\left(\frac{27 x}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{x}{46} \right)}}{529 \left(\cot^{2}{\left(\frac{x}{46} \right)} + 1\right)} - \frac{43740 \cot{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right) \left(\cot^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{4000 \cot{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right)^{2} \left(\cot^{2}{\left(\frac{27 x}{2} \right)} + 1\right)}$$
2
1 21870 19683*atan(10*x) 2000 162000*x 800000*x
----------- - ---------------------- - ---------------- - ----------------------- - ---------------------------- + -----------------------
/x \ / 2\ /pi \ 2 2 3
529*csc|--| \1 + 100*x /*csc(27*x) csc|-- - 27*x| / 2\ / 2\ /pi \ / 2\
\23/ \2 / \1 + 100*x / *csc(27*x) \1 + 100*x / *csc|-- - 27*x| \1 + 100*x / *csc(27*x)
\2 /
$$\frac{800000 x^{2}}{\left(100 x^{2} + 1\right)^{3} \csc{\left(27 x \right)}} - \frac{162000 x}{\left(100 x^{2} + 1\right)^{2} \csc{\left(- 27 x + \frac{\pi}{2} \right)}} - \frac{19683 \operatorname{atan}{\left(10 x \right)}}{\csc{\left(- 27 x + \frac{\pi}{2} \right)}} + \frac{1}{529 \csc{\left(\frac{x}{23} \right)}} - \frac{21870}{\left(100 x^{2} + 1\right) \csc{\left(27 x \right)}} - \frac{2000}{\left(100 x^{2} + 1\right)^{2} \csc{\left(27 x \right)}}$$
2
1 21870 19683*atan(10*x) 2000 162000*x 800000*x
----------- - ---------------------- - ---------------- - ----------------------- - ----------------------- + -----------------------
/x \ / 2\ sec(27*x) 2 2 3
529*csc|--| \1 + 100*x /*csc(27*x) / 2\ / 2\ / 2\
\23/ \1 + 100*x / *csc(27*x) \1 + 100*x / *sec(27*x) \1 + 100*x / *csc(27*x)
$$\frac{800000 x^{2}}{\left(100 x^{2} + 1\right)^{3} \csc{\left(27 x \right)}} - \frac{162000 x}{\left(100 x^{2} + 1\right)^{2} \sec{\left(27 x \right)}} - \frac{19683 \operatorname{atan}{\left(10 x \right)}}{\sec{\left(27 x \right)}} + \frac{1}{529 \csc{\left(\frac{x}{23} \right)}} - \frac{21870}{\left(100 x^{2} + 1\right) \csc{\left(27 x \right)}} - \frac{2000}{\left(100 x^{2} + 1\right)^{2} \csc{\left(27 x \right)}}$$
/ pi x \ / pi\ / pi\ 2 / pi\
cos|- -- + --| 21870*cos|27*x - --| 2000*cos|27*x - --| 800000*x *cos|27*x - --|
\ 2 23/ \ 2 / \ 2 / 162000*x*cos(27*x) \ 2 /
-------------- - -------------------- - 19683*atan(10*x)*cos(27*x) - ------------------- - ------------------ + ------------------------
529 2 2 2 3
1 + 100*x / 2\ / 2\ / 2\
\1 + 100*x / \1 + 100*x / \1 + 100*x /
$$\frac{800000 x^{2} \cos{\left(27 x - \frac{\pi}{2} \right)}}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \cos{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}} - 19683 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} + \frac{\cos{\left(\frac{x}{23} - \frac{\pi}{2} \right)}}{529} - \frac{21870 \cos{\left(27 x - \frac{\pi}{2} \right)}}{100 x^{2} + 1} - \frac{2000 \cos{\left(27 x - \frac{\pi}{2} \right)}}{\left(100 x^{2} + 1\right)^{2}}$$
/x \ /27*x\ / 2/27*x\\ /27*x\ / 2/27*x\\ 2 /27*x\
2*tan|--| 43740*tan|----| 19683*|1 - tan |----||*atan(10*x) 4000*tan|----| 162000*x*|1 - tan |----|| 1600000*x *tan|----|
\46/ \ 2 / \ \ 2 // \ 2 / \ \ 2 // \ 2 /
------------------ - ----------------------------- - --------------------------------- - ------------------------------ - ------------------------------ + ------------------------------
/ 2/x \\ / 2/27*x\\ / 2\ 2/27*x\ 2 2 3
529*|1 + tan |--|| |1 + tan |----||*\1 + 100*x / 1 + tan |----| / 2/27*x\\ / 2\ / 2/27*x\\ / 2\ / 2/27*x\\ / 2\
\ \46// \ \ 2 // \ 2 / |1 + tan |----||*\1 + 100*x / |1 + tan |----||*\1 + 100*x / |1 + tan |----||*\1 + 100*x /
\ \ 2 // \ \ 2 // \ \ 2 //
$$\frac{1600000 x^{2} \tan{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right)^{3} \left(\tan^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{162000 x \left(1 - \tan^{2}{\left(\frac{27 x}{2} \right)}\right)}{\left(100 x^{2} + 1\right)^{2} \left(\tan^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{19683 \left(1 - \tan^{2}{\left(\frac{27 x}{2} \right)}\right) \operatorname{atan}{\left(10 x \right)}}{\tan^{2}{\left(\frac{27 x}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{x}{46} \right)}}{529 \left(\tan^{2}{\left(\frac{x}{46} \right)} + 1\right)} - \frac{43740 \tan{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right) \left(\tan^{2}{\left(\frac{27 x}{2} \right)} + 1\right)} - \frac{4000 \tan{\left(\frac{27 x}{2} \right)}}{\left(100 x^{2} + 1\right)^{2} \left(\tan^{2}{\left(\frac{27 x}{2} \right)} + 1\right)}$$
2
1 21870 19683*atan(10*x) 2000 162000*x 800000*x
------------------ - --------------------------- - ---------------- - ---------------------------- - ----------------------- + ----------------------------
/ pi x \ / 2\ / pi\ sec(27*x) 2 2 3
529*sec|- -- + --| \1 + 100*x /*sec|27*x - --| / 2\ / pi\ / 2\ / 2\ / pi\
\ 2 23/ \ 2 / \1 + 100*x / *sec|27*x - --| \1 + 100*x / *sec(27*x) \1 + 100*x / *sec|27*x - --|
\ 2 / \ 2 /
$$\frac{800000 x^{2}}{\left(100 x^{2} + 1\right)^{3} \sec{\left(27 x - \frac{\pi}{2} \right)}} - \frac{162000 x}{\left(100 x^{2} + 1\right)^{2} \sec{\left(27 x \right)}} - \frac{19683 \operatorname{atan}{\left(10 x \right)}}{\sec{\left(27 x \right)}} + \frac{1}{529 \sec{\left(\frac{x}{23} - \frac{\pi}{2} \right)}} - \frac{21870}{\left(100 x^{2} + 1\right) \sec{\left(27 x - \frac{\pi}{2} \right)}} - \frac{2000}{\left(100 x^{2} + 1\right)^{2} \sec{\left(27 x - \frac{\pi}{2} \right)}}$$
/x \ /pi \
sin|--| 162000*x*sin|-- + 27*x| 2
\23/ 21870*sin(27*x) /pi \ 2000*sin(27*x) \2 / 800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*sin|-- + 27*x| - -------------- - ----------------------- + -------------------
529 2 \2 / 2 2 3
1 + 100*x / 2\ / 2\ / 2\
\1 + 100*x / \1 + 100*x / \1 + 100*x /
$$\frac{800000 x^{2} \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \sin{\left(27 x + \frac{\pi}{2} \right)}}{\left(100 x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{x}{23} \right)}}{529} - 19683 \sin{\left(27 x + \frac{\pi}{2} \right)} \operatorname{atan}{\left(10 x \right)} - \frac{21870 \sin{\left(27 x \right)}}{100 x^{2} + 1} - \frac{2000 \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}}$$
/x \
sin|--| 2
\23/ 21870*sin(27*x) 2000*sin(27*x) 162000*x*cos(27*x) 800000*x *sin(27*x)
------- - --------------- - 19683*atan(10*x)*cos(27*x) - -------------- - ------------------ + -------------------
529 2 2 2 3
1 + 100*x / 2\ / 2\ / 2\
\1 + 100*x / \1 + 100*x / \1 + 100*x /
$$\frac{800000 x^{2} \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{3}} - \frac{162000 x \cos{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}} + \frac{\sin{\left(\frac{x}{23} \right)}}{529} - 19683 \cos{\left(27 x \right)} \operatorname{atan}{\left(10 x \right)} - \frac{21870 \sin{\left(27 x \right)}}{100 x^{2} + 1} - \frac{2000 \sin{\left(27 x \right)}}{\left(100 x^{2} + 1\right)^{2}}$$
sin(x/23)/529 - 21870*sin(27*x)/(1 + 100*x^2) - 19683*atan(10*x)*cos(27*x) - 2000*sin(27*x)/(1 + 100*x^2)^2 - 162000*x*cos(27*x)/(1 + 100*x^2)^2 + 800000*x^2*sin(27*x)/(1 + 100*x^2)^3