Simplificación general
[src]
/ / 6\ / 3\\
2 | 2 2*\1 + 4*x /*atan\2*x /|
6*cot (4*x)*|x *cot(4*x) - -----------------------|
| 2 |
\ sin (4*x) /
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6
1 + 4*x
$$\frac{6 \left(x^{2} \cot{\left(4 x \right)} - \frac{2 \left(4 x^{6} + 1\right) \operatorname{atan}{\left(2 x^{3} \right)}}{\sin^{2}{\left(4 x \right)}}\right) \cot^{2}{\left(4 x \right)}}{4 x^{6} + 1}$$
6*cot(4*x)^2*(x^2*cot(4*x) - 2*(1 + 4*x^6)*atan(2*x^3)/sin(4*x)^2)/(1 + 4*x^6)
cot(4*x)^2*(-12.0 - 12.0*cot(4*x)^2)*atan(2*x^3) + 6.0*x^2*cot(4*x)^3/(1.0 + 4.0*x^6)
cot(4*x)^2*(-12.0 - 12.0*cot(4*x)^2)*atan(2*x^3) + 6.0*x^2*cot(4*x)^3/(1.0 + 4.0*x^6)
Denominador racional
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2 3 2 / 6\ / 2 \ / 3\
6*x *cot (4*x) + cot (4*x)*\1 + 4*x /*\-12 - 12*cot (4*x)/*atan\2*x /
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6
1 + 4*x
$$\frac{6 x^{2} \cot^{3}{\left(4 x \right)} + \left(4 x^{6} + 1\right) \left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)}}{4 x^{6} + 1}$$
(6*x^2*cot(4*x)^3 + cot(4*x)^2*(1 + 4*x^6)*(-12 - 12*cot(4*x)^2)*atan(2*x^3))/(1 + 4*x^6)
Unión de expresiones racionales
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2 / 2 / 6\ / 2 \ / 3\\
6*cot (4*x)*\x *cot(4*x) + 2*\1 + 4*x /*\-1 - cot (4*x)/*atan\2*x //
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6
1 + 4*x
$$\frac{6 \left(x^{2} \cot{\left(4 x \right)} + 2 \left(4 x^{6} + 1\right) \left(- \cot^{2}{\left(4 x \right)} - 1\right) \operatorname{atan}{\left(2 x^{3} \right)}\right) \cot^{2}{\left(4 x \right)}}{4 x^{6} + 1}$$
6*cot(4*x)^2*(x^2*cot(4*x) + 2*(1 + 4*x^6)*(-1 - cot(4*x)^2)*atan(2*x^3))/(1 + 4*x^6)
2 / / 3\ 2 2 / 3\ 6 / 3\ 6 2 / 3\\
-6*cot (4*x)*\2*atan\2*x / - x *cot(4*x) + 2*cot (4*x)*atan\2*x / + 8*x *atan\2*x / + 8*x *cot (4*x)*atan\2*x //
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6
1 + 4*x
$$- \frac{6 \left(8 x^{6} \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)} + 8 x^{6} \operatorname{atan}{\left(2 x^{3} \right)} - x^{2} \cot{\left(4 x \right)} + 2 \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)} + 2 \operatorname{atan}{\left(2 x^{3} \right)}\right) \cot^{2}{\left(4 x \right)}}{4 x^{6} + 1}$$
-6*cot(4*x)^2*(2*atan(2*x^3) - x^2*cot(4*x) + 2*cot(4*x)^2*atan(2*x^3) + 8*x^6*atan(2*x^3) + 8*x^6*cot(4*x)^2*atan(2*x^3))/(1 + 4*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\2*x / 12*atan\2*x / 6*x 20808*cot (x)*atan\2*x / 2640*cot (x)*atan\2*x / 2640*cot (x)*atan\2*x / 1512*x *cot (x) 456*cot (x)*atan\2*x / 108*x *cot (x) 108*x *cot (x) 12*cot (x)*atan\2*x / 12*cot (x)*atan\2*x / 6*x *cot (x) 144*cot (x)*atan\2*x / 144*cot (x)*atan\2*x / 288*cot (x)*atan\2*x / 288*cot (x)*atan\2*x / 666*x *cot (x) 666*x *cot (x) 11232*cot (x)*atan\2*x / 11232*cot (x)*atan\2*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) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*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) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x) - 32*cot (x) + 16*cot (x) + 16*cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*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) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*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) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*x *cot (x) - 192*cot (x) - 64*cot (x) + 64*cot (x) + 192*cot (x) - 768*x *cot (x) - 256*x *cot (x) + 256*x *cot (x) + 768*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{6 x^{2} \cot^{12}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 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{108 x^{2} \cot^{10}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 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{666 x^{2} \cot^{8}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 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{1512 x^{2} \cot^{6}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 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{666 x^{2} \cot^{4}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 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{108 x^{2} \cot^{2}{\left(x \right)}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 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{6 x^{2}}{256 x^{6} \cot^{9}{\left(x \right)} - 768 x^{6} \cot^{7}{\left(x \right)} + 768 x^{6} \cot^{5}{\left(x \right)} - 256 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(2 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(2 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(2 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(2 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(2 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(2 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(2 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(2 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(2 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(2 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(2 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(2 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(2 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(2 x^{3} \right)}}{16 \cot^{6}{\left(x \right)} - 32 \cot^{4}{\left(x \right)} + 16 \cot^{2}{\left(x \right)}}$$
-12*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 12*atan(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 6*x^2/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) - 20808*cot(x)^8*atan(2*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(2*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(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) - 1512*x^2*cot(x)^6/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) - 456*cot(x)^4*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 108*x^2*cot(x)^2/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) - 108*x^2*cot(x)^10/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) - 12*cot(x)^8*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) - 12*cot(x)^16*atan(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 6*x^2*cot(x)^12/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) + 144*cot(x)^2*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) + 144*cot(x)^6*atan(2*x^3)/(-32*cot(x)^4 + 16*cot(x)^2 + 16*cot(x)^6) + 288*cot(x)^2*atan(2*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(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8) + 666*x^2*cot(x)^4/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) + 666*x^2*cot(x)^8/(-192*cot(x)^7 - 64*cot(x)^3 + 64*cot(x)^9 + 192*cot(x)^5 - 768*x^6*cot(x)^7 - 256*x^6*cot(x)^3 + 256*x^6*cot(x)^9 + 768*x^6*cot(x)^5) + 11232*cot(x)^6*atan(2*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(2*x^3)/(-1024*cot(x)^6 - 1024*cot(x)^10 + 256*cot(x)^4 + 256*cot(x)^12 + 1536*cot(x)^8)
2 3
2 / 3\ 4 / 3\ 6*x *cot (4*x)
- 12*cot (4*x)*atan\2*x / - 12*cot (4*x)*atan\2*x / + --------------
6
1 + 4*x
$$\frac{6 x^{2} \cot^{3}{\left(4 x \right)}}{4 x^{6} + 1} - 12 \cot^{4}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)} - 12 \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x^{3} \right)}$$
-12*cot(4*x)^2*atan(2*x^3) - 12*cot(4*x)^4*atan(2*x^3) + 6*x^2*cot(4*x)^3/(1 + 4*x^6)