Simplificación general
[src]
/ / 6\ / 3\\
2 | 2 4*\1 + x /*atan\x /|
3*cot (4*x)*|x *cot(4*x) - -------------------|
| 2 |
\ sin (4*x) /
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6
1 + x
$$\frac{3 \left(x^{2} \cot{\left(4 x \right)} - \frac{4 \left(x^{6} + 1\right) \operatorname{atan}{\left(x^{3} \right)}}{\sin^{2}{\left(4 x \right)}}\right) \cot^{2}{\left(4 x \right)}}{x^{6} + 1}$$
3*cot(4*x)^2*(x^2*cot(4*x) - 4*(1 + x^6)*atan(x^3)/sin(4*x)^2)/(1 + x^6)
cot(4*x)^2*(-12.0 - 12.0*cot(4*x)^2)*atan(x^3) + 3.0*x^2*cot(4*x)^3/(1.0 + x^6)
cot(4*x)^2*(-12.0 - 12.0*cot(4*x)^2)*atan(x^3) + 3.0*x^2*cot(4*x)^3/(1.0 + x^6)
Unión de expresiones racionales
[src]
2 / 2 / 6\ / 2 \ / 3\\
3*cot (4*x)*\x *cot(4*x) + 4*\1 + x /*\-1 - cot (4*x)/*atan\x //
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6
1 + x
$$\frac{3 \left(x^{2} \cot{\left(4 x \right)} + 4 \left(x^{6} + 1\right) \left(- \cot^{2}{\left(4 x \right)} - 1\right) \operatorname{atan}{\left(x^{3} \right)}\right) \cot^{2}{\left(4 x \right)}}{x^{6} + 1}$$
3*cot(4*x)^2*(x^2*cot(4*x) + 4*(1 + x^6)*(-1 - cot(4*x)^2)*atan(x^3))/(1 + x^6)
2 3
2 / 3\ 4 / 3\ 3*x *cot (4*x)
- 12*cot (4*x)*atan\x / - 12*cot (4*x)*atan\x / + --------------
6
1 + x
$$\frac{3 x^{2} \cot^{3}{\left(4 x \right)}}{x^{6} + 1} - 12 \cot^{4}{\left(4 x \right)} \operatorname{atan}{\left(x^{3} \right)} - 12 \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(x^{3} \right)}$$
-12*cot(4*x)^2*atan(x^3) - 12*cot(4*x)^4*atan(x^3) + 3*x^2*cot(4*x)^3/(1 + x^6)
2 / / 3\ 2 6 / 3\ 2 / 3\ 6 2 / 3\\
-3*cot (4*x)*\4*atan\x / - x *cot(4*x) + 4*x *atan\x / + 4*cot (4*x)*atan\x / + 4*x *cot (4*x)*atan\x //
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/ 2\ / 4 2\
\1 + x /*\1 + x - x /
$$- \frac{3 \left(4 x^{6} \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(x^{3} \right)} + 4 x^{6} \operatorname{atan}{\left(x^{3} \right)} - x^{2} \cot{\left(4 x \right)} + 4 \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(x^{3} \right)} + 4 \operatorname{atan}{\left(x^{3} \right)}\right) \cot^{2}{\left(4 x \right)}}{\left(x^{2} + 1\right) \left(x^{4} - x^{2} + 1\right)}$$
-3*cot(4*x)^2*(4*atan(x^3) - x^2*cot(4*x) + 4*x^6*atan(x^3) + 4*cot(4*x)^2*atan(x^3) + 4*x^6*cot(4*x)^2*atan(x^3))/((1 + x^2)*(1 + x^4 - x^2))
Denominador racional
[src]
2 3 2 / 6\ / 2 \ / 3\
3*x *cot (4*x) + cot (4*x)*\1 + x /*\-12 - 12*cot (4*x)/*atan\x /
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6
1 + x
$$\frac{3 x^{2} \cot^{3}{\left(4 x \right)} + \left(x^{6} + 1\right) \left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(x^{3} \right)}}{x^{6} + 1}$$
(3*x^2*cot(4*x)^3 + cot(4*x)^2*(1 + x^6)*(-12 - 12*cot(4*x)^2)*atan(x^3))/(1 + x^6)
Abrimos la expresión
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/ 3\ / 3\ 2 8 / 3\ 4 / 3\ 12 / 3\ 2 6 4 / 3\ 2 2 2 10 8 / 3\ 16 / 3\ 2 12 2 / 3\ 6 / 3\ 2 / 3\ 14 / 3\ 2 4 2 8 6 / 3\ 10 / 3\
12*atan\x / 12*atan\x / 3*x 20808*cot (x)*atan\x / 2640*cot (x)*atan\x / 2640*cot (x)*atan\x / 756*x *cot (x) 456*cot (x)*atan\x / 54*x *cot (x) 54*x *cot (x) 12*cot (x)*atan\x / 12*cot (x)*atan\x / 3*x *cot (x) 144*cot (x)*atan\x / 144*cot (x)*atan\x / 288*cot (x)*atan\x / 288*cot (x)*atan\x / 333*x *cot (x) 333*x *cot (x) 11232*cot (x)*atan\x / 11232*cot (x)*atan\x /
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- 32*cot (x) + 16*cot (x) + 16*cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 192*x *cot (x) - 64*x *cot (x) + 64*x *cot (x) + 192*x *cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 192*x *cot (x) - 64*x *cot (x) + 64*x *cot (x) + 192*x *cot (x) - 32*cot (x) + 16*cot (x) + 16*cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 192*x *cot (x) - 64*x *cot (x) + 64*x *cot (x) + 192*x *cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 192*x *cot (x) - 64*x *cot (x) + 64*x *cot (x) + 192*x *cot (x) - 32*cot (x) + 16*cot (x) + 16*cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 192*x *cot (x) - 64*x *cot (x) + 64*x *cot (x) + 192*x *cot (x) - 32*cot (x) + 16*cot (x) + 16*cot (x) - 32*cot (x) + 16*cot (x) + 16*cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 192*x *cot (x) - 64*x *cot (x) + 64*x *cot (x) + 192*x *cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 192*x *cot (x) - 64*x *cot (x) + 64*x *cot (x) + 192*x *cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x) - 1024*cot (x) - 1024*cot (x) + 256*cot (x) + 256*cot (x) + 1536*cot (x)
$$\frac{3 x^{2} \cot^{12}{\left(x \right)}}{64 x^{6} \cot^{9}{\left(x \right)} - 192 x^{6} \cot^{7}{\left(x \right)} + 192 x^{6} \cot^{5}{\left(x \right)} - 64 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} - \frac{54 x^{2} \cot^{10}{\left(x \right)}}{64 x^{6} \cot^{9}{\left(x \right)} - 192 x^{6} \cot^{7}{\left(x \right)} + 192 x^{6} \cot^{5}{\left(x \right)} - 64 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} + \frac{333 x^{2} \cot^{8}{\left(x \right)}}{64 x^{6} \cot^{9}{\left(x \right)} - 192 x^{6} \cot^{7}{\left(x \right)} + 192 x^{6} \cot^{5}{\left(x \right)} - 64 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} - \frac{756 x^{2} \cot^{6}{\left(x \right)}}{64 x^{6} \cot^{9}{\left(x \right)} - 192 x^{6} \cot^{7}{\left(x \right)} + 192 x^{6} \cot^{5}{\left(x \right)} - 64 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} + \frac{333 x^{2} \cot^{4}{\left(x \right)}}{64 x^{6} \cot^{9}{\left(x \right)} - 192 x^{6} \cot^{7}{\left(x \right)} + 192 x^{6} \cot^{5}{\left(x \right)} - 64 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} - \frac{54 x^{2} \cot^{2}{\left(x \right)}}{64 x^{6} \cot^{9}{\left(x \right)} - 192 x^{6} \cot^{7}{\left(x \right)} + 192 x^{6} \cot^{5}{\left(x \right)} - 64 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} + \frac{3 x^{2}}{64 x^{6} \cot^{9}{\left(x \right)} - 192 x^{6} \cot^{7}{\left(x \right)} + 192 x^{6} \cot^{5}{\left(x \right)} - 64 x^{6} \cot^{3}{\left(x \right)} + 64 \cot^{9}{\left(x \right)} - 192 \cot^{7}{\left(x \right)} + 192 \cot^{5}{\left(x \right)} - 64 \cot^{3}{\left(x \right)}} - \frac{12 \cot^{16}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} + \frac{288 \cot^{14}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{2640 \cot^{12}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} + \frac{11232 \cot^{10}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{20808 \cot^{8}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} + \frac{11232 \cot^{6}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{2640 \cot^{4}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} + \frac{288 \cot^{2}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{12 \operatorname{atan}{\left(x^{3} \right)}}{256 \cot^{12}{\left(x \right)} - 1024 \cot^{10}{\left(x \right)} + 1536 \cot^{8}{\left(x \right)} - 1024 \cot^{6}{\left(x \right)} + 256 \cot^{4}{\left(x \right)}} - \frac{12 \cot^{8}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}} + \frac{144 \cot^{6}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}} - \frac{456 \cot^{4}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}} + \frac{144 \cot^{2}{\left(x \right)} \operatorname{atan}{\left(x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}} - \frac{12 \operatorname{atan}{\left(x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}}$$
-12*atan(x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 12*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 3*x^2/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 192*x^6*cot(x)^7 - 64*x^6*cot(x)^3 + 64*x^6*cot(x)^9 + 192*x^6*cot(x)^5) - 20808*cot(x)^8*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 2640*cot(x)^4*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 2640*cot(x)^12*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 756*x^2*cot(x)^6/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 192*x^6*cot(x)^7 - 64*x^6*cot(x)^3 + 64*x^6*cot(x)^9 + 192*x^6*cot(x)^5) - 456*cot(x)^4*atan(x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 54*x^2*cot(x)^2/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 192*x^6*cot(x)^7 - 64*x^6*cot(x)^3 + 64*x^6*cot(x)^9 + 192*x^6*cot(x)^5) - 54*x^2*cot(x)^10/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 192*x^6*cot(x)^7 - 64*x^6*cot(x)^3 + 64*x^6*cot(x)^9 + 192*x^6*cot(x)^5) - 12*cot(x)^8*atan(x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 12*cot(x)^16*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 3*x^2*cot(x)^12/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 192*x^6*cot(x)^7 - 64*x^6*cot(x)^3 + 64*x^6*cot(x)^9 + 192*x^6*cot(x)^5) + 144*cot(x)^2*atan(x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) + 144*cot(x)^6*atan(x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) + 288*cot(x)^2*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 288*cot(x)^14*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 333*x^2*cot(x)^4/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 192*x^6*cot(x)^7 - 64*x^6*cot(x)^3 + 64*x^6*cot(x)^9 + 192*x^6*cot(x)^5) + 333*x^2*cot(x)^8/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 192*x^6*cot(x)^7 - 64*x^6*cot(x)^3 + 64*x^6*cot(x)^9 + 192*x^6*cot(x)^5) + 11232*cot(x)^6*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 11232*cot(x)^10*atan(x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8)