3.89.98 \(\int \frac {-3125000+30625000 x-124875000 x^2+269500000 x^3-319025000 x^4+183897000 x^5-22013600 x^6-14862680 x^7-2972536 x^9+880544 x^{10}+1471176 x^{11}+510440 x^{12}+86240 x^{13}+7992 x^{14}+392 x^{15}+8 x^{16}+(-15000 x^4+63000 x^5-82200 x^6+28560 x^7+5712 x^9+3288 x^{10}+504 x^{11}+24 x^{12}+e^5 (-5000 x^4+21000 x^5-27400 x^6+9520 x^7+1904 x^9+1096 x^{10}+168 x^{11}+8 x^{12})) \log ^8(4)}{3 x^9 \log ^{16}(4)} \, dx\)

Optimal. Leaf size=28 \[ \frac {1}{3} \left (3+e^5+\frac {\left (-7+\frac {5}{x}-x\right )^4}{\log ^8(4)}\right )^2 \]

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Rubi [B]  time = 0.22, antiderivative size = 303, normalized size of antiderivative = 10.82, number of steps used = 3, number of rules used = 2, integrand size = 177, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {12, 14} \begin {gather*} \frac {x^8}{3 \log ^{16}(4)}+\frac {390625}{3 x^8 \log ^{16}(4)}+\frac {56 x^7}{3 \log ^{16}(4)}-\frac {4375000}{3 x^7 \log ^{16}(4)}+\frac {444 x^6}{\log ^{16}(4)}+\frac {6937500}{x^6 \log ^{16}(4)}+\frac {17248 x^5}{3 \log ^{16}(4)}-\frac {53900000}{3 x^5 \log ^{16}(4)}+\frac {2 x^4 \left (63805+3 \log ^8(4)+e^5 \log ^8(4)\right )}{3 \log ^{16}(4)}+\frac {1250 \left (63805+3 \log ^8(4)+e^5 \log ^8(4)\right )}{3 x^4 \log ^{16}(4)}+\frac {56 x^3 \left (8757+3 \log ^8(4)+e^5 \log ^8(4)\right )}{3 \log ^{16}(4)}-\frac {7000 \left (8757+3 \log ^8(4)+e^5 \log ^8(4)\right )}{3 x^3 \log ^{16}(4)}+\frac {4 x^2 \left (110068+411 \log ^8(4)+137 e^5 \log ^8(4)\right )}{3 \log ^{16}(4)}+\frac {100 \left (110068+411 \log ^8(4)+137 e^5 \log ^8(4)\right )}{3 x^2 \log ^{16}(4)}-\frac {56 x \left (53081-102 \log ^8(4)-34 e^5 \log ^8(4)\right )}{3 \log ^{16}(4)}+\frac {280 \left (53081-102 \log ^8(4)-34 e^5 \log ^8(4)\right )}{3 x \log ^{16}(4)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-3125000 + 30625000*x - 124875000*x^2 + 269500000*x^3 - 319025000*x^4 + 183897000*x^5 - 22013600*x^6 - 14
862680*x^7 - 2972536*x^9 + 880544*x^10 + 1471176*x^11 + 510440*x^12 + 86240*x^13 + 7992*x^14 + 392*x^15 + 8*x^
16 + (-15000*x^4 + 63000*x^5 - 82200*x^6 + 28560*x^7 + 5712*x^9 + 3288*x^10 + 504*x^11 + 24*x^12 + E^5*(-5000*
x^4 + 21000*x^5 - 27400*x^6 + 9520*x^7 + 1904*x^9 + 1096*x^10 + 168*x^11 + 8*x^12))*Log[4]^8)/(3*x^9*Log[4]^16
),x]

[Out]

390625/(3*x^8*Log[4]^16) - 4375000/(3*x^7*Log[4]^16) + 6937500/(x^6*Log[4]^16) - 53900000/(3*x^5*Log[4]^16) +
(17248*x^5)/(3*Log[4]^16) + (444*x^6)/Log[4]^16 + (56*x^7)/(3*Log[4]^16) + x^8/(3*Log[4]^16) + (280*(53081 - 1
02*Log[4]^8 - 34*E^5*Log[4]^8))/(3*x*Log[4]^16) - (56*x*(53081 - 102*Log[4]^8 - 34*E^5*Log[4]^8))/(3*Log[4]^16
) - (7000*(8757 + 3*Log[4]^8 + E^5*Log[4]^8))/(3*x^3*Log[4]^16) + (56*x^3*(8757 + 3*Log[4]^8 + E^5*Log[4]^8))/
(3*Log[4]^16) + (1250*(63805 + 3*Log[4]^8 + E^5*Log[4]^8))/(3*x^4*Log[4]^16) + (2*x^4*(63805 + 3*Log[4]^8 + E^
5*Log[4]^8))/(3*Log[4]^16) + (100*(110068 + 411*Log[4]^8 + 137*E^5*Log[4]^8))/(3*x^2*Log[4]^16) + (4*x^2*(1100
68 + 411*Log[4]^8 + 137*E^5*Log[4]^8))/(3*Log[4]^16)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-3125000+30625000 x-124875000 x^2+269500000 x^3-319025000 x^4+183897000 x^5-22013600 x^6-14862680 x^7-2972536 x^9+880544 x^{10}+1471176 x^{11}+510440 x^{12}+86240 x^{13}+7992 x^{14}+392 x^{15}+8 x^{16}+\left (-15000 x^4+63000 x^5-82200 x^6+28560 x^7+5712 x^9+3288 x^{10}+504 x^{11}+24 x^{12}+e^5 \left (-5000 x^4+21000 x^5-27400 x^6+9520 x^7+1904 x^9+1096 x^{10}+168 x^{11}+8 x^{12}\right )\right ) \log ^8(4)}{x^9} \, dx}{3 \log ^{16}(4)}\\ &=\frac {\int \left (-\frac {3125000}{x^9}+\frac {30625000}{x^8}-\frac {124875000}{x^7}+\frac {269500000}{x^6}+86240 x^4+7992 x^5+392 x^6+8 x^7+\frac {21000 \left (8757+3 \log ^8(4)+e^5 \log ^8(4)\right )}{x^4}+168 x^2 \left (8757+3 \log ^8(4)+e^5 \log ^8(4)\right )-\frac {5000 \left (63805+3 \log ^8(4)+e^5 \log ^8(4)\right )}{x^5}+8 x^3 \left (63805+3 \log ^8(4)+e^5 \log ^8(4)\right )+56 \left (-53081+102 \log ^8(4)+34 e^5 \log ^8(4)\right )+\frac {280 \left (-53081+102 \log ^8(4)+34 e^5 \log ^8(4)\right )}{x^2}-\frac {200 \left (110068+411 \log ^8(4)+137 e^5 \log ^8(4)\right )}{x^3}+8 x \left (110068+411 \log ^8(4)+137 e^5 \log ^8(4)\right )\right ) \, dx}{3 \log ^{16}(4)}\\ &=\frac {390625}{3 x^8 \log ^{16}(4)}-\frac {4375000}{3 x^7 \log ^{16}(4)}+\frac {6937500}{x^6 \log ^{16}(4)}-\frac {53900000}{3 x^5 \log ^{16}(4)}+\frac {17248 x^5}{3 \log ^{16}(4)}+\frac {444 x^6}{\log ^{16}(4)}+\frac {56 x^7}{3 \log ^{16}(4)}+\frac {x^8}{3 \log ^{16}(4)}+\frac {280 \left (53081-102 \log ^8(4)-34 e^5 \log ^8(4)\right )}{3 x \log ^{16}(4)}-\frac {56 x \left (53081-102 \log ^8(4)-34 e^5 \log ^8(4)\right )}{3 \log ^{16}(4)}-\frac {7000 \left (8757+3 \log ^8(4)+e^5 \log ^8(4)\right )}{3 x^3 \log ^{16}(4)}+\frac {56 x^3 \left (8757+3 \log ^8(4)+e^5 \log ^8(4)\right )}{3 \log ^{16}(4)}+\frac {1250 \left (63805+3 \log ^8(4)+e^5 \log ^8(4)\right )}{3 x^4 \log ^{16}(4)}+\frac {2 x^4 \left (63805+3 \log ^8(4)+e^5 \log ^8(4)\right )}{3 \log ^{16}(4)}+\frac {100 \left (110068+411 \log ^8(4)+137 e^5 \log ^8(4)\right )}{3 x^2 \log ^{16}(4)}+\frac {4 x^2 \left (110068+411 \log ^8(4)+137 e^5 \log ^8(4)\right )}{3 \log ^{16}(4)}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.06, size = 216, normalized size = 7.71 \begin {gather*} \frac {390625-4375000 x+20812500 x^2-53900000 x^3+17248 x^{13}+1332 x^{14}+56 x^{15}+x^{16}-7000 x^5 \left (8757+3 \log ^8(4)+e^5 \log ^8(4)\right )+56 x^{11} \left (8757+3 \log ^8(4)+e^5 \log ^8(4)\right )+1250 x^4 \left (63805+3 \log ^8(4)+e^5 \log ^8(4)\right )+2 x^{12} \left (63805+3 \log ^8(4)+e^5 \log ^8(4)\right )-280 x^7 \left (-53081+102 \log ^8(4)+34 e^5 \log ^8(4)\right )+56 x^9 \left (-53081+102 \log ^8(4)+34 e^5 \log ^8(4)\right )+100 x^6 \left (110068+411 \log ^8(4)+137 e^5 \log ^8(4)\right )+4 x^{10} \left (110068+411 \log ^8(4)+137 e^5 \log ^8(4)\right )}{3 x^8 \log ^{16}(4)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3125000 + 30625000*x - 124875000*x^2 + 269500000*x^3 - 319025000*x^4 + 183897000*x^5 - 22013600*x^
6 - 14862680*x^7 - 2972536*x^9 + 880544*x^10 + 1471176*x^11 + 510440*x^12 + 86240*x^13 + 7992*x^14 + 392*x^15
+ 8*x^16 + (-15000*x^4 + 63000*x^5 - 82200*x^6 + 28560*x^7 + 5712*x^9 + 3288*x^10 + 504*x^11 + 24*x^12 + E^5*(
-5000*x^4 + 21000*x^5 - 27400*x^6 + 9520*x^7 + 1904*x^9 + 1096*x^10 + 168*x^11 + 8*x^12))*Log[4]^8)/(3*x^9*Log
[4]^16),x]

[Out]

(390625 - 4375000*x + 20812500*x^2 - 53900000*x^3 + 17248*x^13 + 1332*x^14 + 56*x^15 + x^16 - 7000*x^5*(8757 +
3*Log[4]^8 + E^5*Log[4]^8) + 56*x^11*(8757 + 3*Log[4]^8 + E^5*Log[4]^8) + 1250*x^4*(63805 + 3*Log[4]^8 + E^5*
Log[4]^8) + 2*x^12*(63805 + 3*Log[4]^8 + E^5*Log[4]^8) - 280*x^7*(-53081 + 102*Log[4]^8 + 34*E^5*Log[4]^8) + 5
6*x^9*(-53081 + 102*Log[4]^8 + 34*E^5*Log[4]^8) + 100*x^6*(110068 + 411*Log[4]^8 + 137*E^5*Log[4]^8) + 4*x^10*
(110068 + 411*Log[4]^8 + 137*E^5*Log[4]^8))/(3*x^8*Log[4]^16)

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fricas [B]  time = 0.50, size = 171, normalized size = 6.11 \begin {gather*} \frac {x^{16} + 56 \, x^{15} + 1332 \, x^{14} + 17248 \, x^{13} + 127610 \, x^{12} + 490392 \, x^{11} + 440272 \, x^{10} - 2972536 \, x^{9} + 512 \, {\left (3 \, x^{12} + 84 \, x^{11} + 822 \, x^{10} + 2856 \, x^{9} - 14280 \, x^{7} + 20550 \, x^{6} - 10500 \, x^{5} + 1875 \, x^{4} + {\left (x^{12} + 28 \, x^{11} + 274 \, x^{10} + 952 \, x^{9} - 4760 \, x^{7} + 6850 \, x^{6} - 3500 \, x^{5} + 625 \, x^{4}\right )} e^{5}\right )} \log \relax (2)^{8} + 14862680 \, x^{7} + 11006800 \, x^{6} - 61299000 \, x^{5} + 79756250 \, x^{4} - 53900000 \, x^{3} + 20812500 \, x^{2} - 4375000 \, x + 390625}{196608 \, x^{8} \log \relax (2)^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/196608*(256*((8*x^12+168*x^11+1096*x^10+1904*x^9+9520*x^7-27400*x^6+21000*x^5-5000*x^4)*exp(5)+24*
x^12+504*x^11+3288*x^10+5712*x^9+28560*x^7-82200*x^6+63000*x^5-15000*x^4)*log(2)^8+8*x^16+392*x^15+7992*x^14+8
6240*x^13+510440*x^12+1471176*x^11+880544*x^10-2972536*x^9-14862680*x^7-22013600*x^6+183897000*x^5-319025000*x
^4+269500000*x^3-124875000*x^2+30625000*x-3125000)/x^9/log(2)^16,x, algorithm="fricas")

[Out]

1/196608*(x^16 + 56*x^15 + 1332*x^14 + 17248*x^13 + 127610*x^12 + 490392*x^11 + 440272*x^10 - 2972536*x^9 + 51
2*(3*x^12 + 84*x^11 + 822*x^10 + 2856*x^9 - 14280*x^7 + 20550*x^6 - 10500*x^5 + 1875*x^4 + (x^12 + 28*x^11 + 2
74*x^10 + 952*x^9 - 4760*x^7 + 6850*x^6 - 3500*x^5 + 625*x^4)*e^5)*log(2)^8 + 14862680*x^7 + 11006800*x^6 - 61
299000*x^5 + 79756250*x^4 - 53900000*x^3 + 20812500*x^2 - 4375000*x + 390625)/(x^8*log(2)^16)

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giac [B]  time = 0.19, size = 239, normalized size = 8.54 \begin {gather*} \frac {512 \, x^{4} e^{5} \log \relax (2)^{8} + 1536 \, x^{4} \log \relax (2)^{8} + 14336 \, x^{3} e^{5} \log \relax (2)^{8} + 43008 \, x^{3} \log \relax (2)^{8} + 140288 \, x^{2} e^{5} \log \relax (2)^{8} + 420864 \, x^{2} \log \relax (2)^{8} + 487424 \, x e^{5} \log \relax (2)^{8} + 1462272 \, x \log \relax (2)^{8} + x^{8} + 56 \, x^{7} + 1332 \, x^{6} + 17248 \, x^{5} + 127610 \, x^{4} + 490392 \, x^{3} + 440272 \, x^{2} - 2972536 \, x - \frac {5 \, {\left (487424 \, x^{7} e^{5} \log \relax (2)^{8} + 1462272 \, x^{7} \log \relax (2)^{8} - 701440 \, x^{6} e^{5} \log \relax (2)^{8} - 2104320 \, x^{6} \log \relax (2)^{8} + 358400 \, x^{5} e^{5} \log \relax (2)^{8} + 1075200 \, x^{5} \log \relax (2)^{8} - 64000 \, x^{4} e^{5} \log \relax (2)^{8} - 192000 \, x^{4} \log \relax (2)^{8} - 2972536 \, x^{7} - 2201360 \, x^{6} + 12259800 \, x^{5} - 15951250 \, x^{4} + 10780000 \, x^{3} - 4162500 \, x^{2} + 875000 \, x - 78125\right )}}{x^{8}}}{196608 \, \log \relax (2)^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/196608*(256*((8*x^12+168*x^11+1096*x^10+1904*x^9+9520*x^7-27400*x^6+21000*x^5-5000*x^4)*exp(5)+24*
x^12+504*x^11+3288*x^10+5712*x^9+28560*x^7-82200*x^6+63000*x^5-15000*x^4)*log(2)^8+8*x^16+392*x^15+7992*x^14+8
6240*x^13+510440*x^12+1471176*x^11+880544*x^10-2972536*x^9-14862680*x^7-22013600*x^6+183897000*x^5-319025000*x
^4+269500000*x^3-124875000*x^2+30625000*x-3125000)/x^9/log(2)^16,x, algorithm="giac")

[Out]

1/196608*(512*x^4*e^5*log(2)^8 + 1536*x^4*log(2)^8 + 14336*x^3*e^5*log(2)^8 + 43008*x^3*log(2)^8 + 140288*x^2*
e^5*log(2)^8 + 420864*x^2*log(2)^8 + 487424*x*e^5*log(2)^8 + 1462272*x*log(2)^8 + x^8 + 56*x^7 + 1332*x^6 + 17
248*x^5 + 127610*x^4 + 490392*x^3 + 440272*x^2 - 2972536*x - 5*(487424*x^7*e^5*log(2)^8 + 1462272*x^7*log(2)^8
- 701440*x^6*e^5*log(2)^8 - 2104320*x^6*log(2)^8 + 358400*x^5*e^5*log(2)^8 + 1075200*x^5*log(2)^8 - 64000*x^4
*e^5*log(2)^8 - 192000*x^4*log(2)^8 - 2972536*x^7 - 2201360*x^6 + 12259800*x^5 - 15951250*x^4 + 10780000*x^3 -
4162500*x^2 + 875000*x - 78125)/x^8)/log(2)^16

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maple [B]  time = 0.18, size = 226, normalized size = 8.07

method	result	size
default	\(\frac {64 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{4}+1792 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{3}+192 \ln \relax (2)^{8} x^{4}+17536 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{2}+5376 \ln \relax (2)^{8} x^{3}+60928 \,{\mathrm e}^{5} \ln \relax (2)^{8} x +52608 \ln \relax (2)^{8} x^{2}+182784 x \ln \relax (2)^{8}+\frac {x^{8}}{8}+7 x^{7}+\frac {333 x^{6}}{2}+2156 x^{5}+\frac {63805 x^{4}}{4}+61299 x^{3}+55034 x^{2}-371567 x +\frac {390625}{8 x^{8}}-\frac {-160000 \,{\mathrm e}^{5} \ln \relax (2)^{8}-480000 \ln \relax (2)^{8}-39878125}{4 x^{4}}-\frac {6737500}{x^{5}}+\frac {5203125}{2 x^{6}}-\frac {-876800 \,{\mathrm e}^{5} \ln \relax (2)^{8}-2630400 \ln \relax (2)^{8}-2751700}{2 x^{2}}-\frac {304640 \,{\mathrm e}^{5} \ln \relax (2)^{8}+913920 \ln \relax (2)^{8}-1857835}{x}-\frac {672000 \,{\mathrm e}^{5} \ln \relax (2)^{8}+2016000 \ln \relax (2)^{8}[phone]}{3 x^{3}}-\frac {546875}{x^{7}}}{24576 \ln \relax (2)^{16}}\)	\(226\)
gosper	\(\frac {390625-4375000 x +1462272 x^{9} \ln \relax (2)^{8}+490392 x^{11}+127610 x^{12}+17248 x^{13}+1332 x^{14}+x^{16}+56 x^{15}[phone] x^{7}+440272 x^{10}-2972536 x^{9}[phone] x^{6}-61299000 x^{5}[phone] x^{4}-53900000 x^{3}[phone] x^{2}-7311360 x^{7} \ln \relax (2)^{8}+420864 x^{10} \ln \relax (2)^{8}+512 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{12}+14336 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{11}[phone] \ln \relax (2)^{8} x^{6}-5376000 \ln \relax (2)^{8} x^{5}+960000 \ln \relax (2)^{8} x^{4}-1792000 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{5}+3507200 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{6}+320000 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{4}+140288 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{10}+487424 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{9}-2437120 \,{\mathrm e}^{5} \ln \relax (2)^{8} x^{7}+1536 \ln \relax (2)^{8} x^{12}+43008 \ln \relax (2)^{8} x^{11}}{196608 \ln \relax (2)^{16} x^{8}}\)	\(243\)
risch	\(\frac {{\mathrm e}^{5} x^{4}}{384 \ln \relax (2)^{8}}+\frac {7 \,{\mathrm e}^{5} x^{3}}{96 \ln \relax (2)^{8}}+\frac {x^{4}}{128 \ln \relax (2)^{8}}+\frac {137 \,{\mathrm e}^{5} x^{2}}{192 \ln \relax (2)^{8}}+\frac {7 x^{3}}{32 \ln \relax (2)^{8}}+\frac {119 \,{\mathrm e}^{5} x}{48 \ln \relax (2)^{8}}+\frac {137 x^{2}}{64 \ln \relax (2)^{8}}+\frac {119 x}{16 \ln \relax (2)^{8}}+\frac {x^{8}}{196608 \ln \relax (2)^{16}}+\frac {7 x^{7}}{24576 \ln \relax (2)^{16}}+\frac {111 x^{6}}{16384 \ln \relax (2)^{16}}+\frac {539 x^{5}}{6144 \ln \relax (2)^{16}}+\frac {63805 x^{4}}{98304 \ln \relax (2)^{16}}+\frac {20433 x^{3}}{8192 \ln \relax (2)^{16}}+\frac {27517 x^{2}}{12288 \ln \relax (2)^{16}}-\frac {371567 x}{24576 \ln \relax (2)^{16}}+\frac {\left (-2437120 \,{\mathrm e}^{5} \ln \relax (2)^{8}-7311360 \ln \relax (2)^{8}[phone]\right ) x^{7}+\left (3507200 \,{\mathrm e}^{5} \ln \relax (2)^{8}[phone] \ln \relax (2)^{8}[phone]\right ) x^{6}+\left (-1792000 \,{\mathrm e}^{5} \ln \relax (2)^{8}-5376000 \ln \relax (2)^{8}-61299000\right ) x^{5}+\left (320000 \,{\mathrm e}^{5} \ln \relax (2)^{8}+960000 \ln \relax (2)^{8}[phone]\right ) x^{4}-53900000 x^{3}[phone] x^{2}-4375000 x +390625}{196608 \ln \relax (2)^{16} x^{8}}\)	\(252\)
norman	\(\frac {\frac {390625}{196608 \ln \relax (2)}-\frac {546875 x}{24576 \ln \relax (2)}+\frac {1734375 x^{2}}{16384 \ln \relax (2)}-\frac {1684375 x^{3}}{6144 \ln \relax (2)}+\frac {539 x^{13}}{6144 \ln \relax (2)}+\frac {111 x^{14}}{16384 \ln \relax (2)}+\frac {7 x^{15}}{24576 \ln \relax (2)}+\frac {x^{16}}{196608 \ln \relax (2)}-\frac {875 \left (256 \,{\mathrm e}^{5} \ln \relax (2)^{8}+768 \ln \relax (2)^{8}+8757\right ) x^{5}}{24576 \ln \relax (2)}+\frac {7 \left (256 \,{\mathrm e}^{5} \ln \relax (2)^{8}+768 \ln \relax (2)^{8}+8757\right ) x^{11}}{24576 \ln \relax (2)}+\frac {625 \left (256 \,{\mathrm e}^{5} \ln \relax (2)^{8}+768 \ln \relax (2)^{8}+63805\right ) x^{4}}{98304 \ln \relax (2)}+\frac {\left (256 \,{\mathrm e}^{5} \ln \relax (2)^{8}+768 \ln \relax (2)^{8}+63805\right ) x^{12}}{98304 \ln \relax (2)}-\frac {35 \left (8704 \,{\mathrm e}^{5} \ln \relax (2)^{8}+26112 \ln \relax (2)^{8}-53081\right ) x^{7}}{24576 \ln \relax (2)}+\frac {7 \left (8704 \,{\mathrm e}^{5} \ln \relax (2)^{8}+26112 \ln \relax (2)^{8}-53081\right ) x^{9}}{24576 \ln \relax (2)}+\frac {25 \left (8768 \,{\mathrm e}^{5} \ln \relax (2)^{8}+26304 \ln \relax (2)^{8}+27517\right ) x^{6}}{12288 \ln \relax (2)}+\frac {\left (8768 \,{\mathrm e}^{5} \ln \relax (2)^{8}+26304 \ln \relax (2)^{8}+27517\right ) x^{10}}{12288 \ln \relax (2)}}{x^{8} \ln \relax (2)^{15}}\)	\(277\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/196608*(256*((8*x^12+168*x^11+1096*x^10+1904*x^9+9520*x^7-27400*x^6+21000*x^5-5000*x^4)*exp(5)+24*x^12+5
04*x^11+3288*x^10+5712*x^9+28560*x^7-82200*x^6+63000*x^5-15000*x^4)*ln(2)^8+8*x^16+392*x^15+7992*x^14+86240*x^
13+510440*x^12+1471176*x^11+880544*x^10-2972536*x^9-14862680*x^7-22013600*x^6+183897000*x^5-319025000*x^4+2695
00000*x^3-124875000*x^2+30625000*x-3125000)/x^9/ln(2)^16,x,method=_RETURNVERBOSE)

[Out]

1/24576/ln(2)^16*(64*exp(5)*ln(2)^8*x^4+1792*exp(5)*ln(2)^8*x^3+192*ln(2)^8*x^4+17536*exp(5)*ln(2)^8*x^2+5376*
ln(2)^8*x^3+60928*exp(5)*ln(2)^8*x+52608*ln(2)^8*x^2+182784*x*ln(2)^8+1/8*x^8+7*x^7+333/2*x^6+2156*x^5+63805/4
*x^4+61299*x^3+55034*x^2-371567*x+390625/8/x^8-1/4*(-160000*exp(5)*ln(2)^8-480000*ln(2)^8-39878125)/x^4-673750
0/x^5+5203125/2/x^6-1/2*(-876800*exp(5)*ln(2)^8-2630400*ln(2)^8-2751700)/x^2-(304640*exp(5)*ln(2)^8+913920*ln(
2)^8-1857835)/x-1/3*(672000*exp(5)*ln(2)^8+2016000*ln(2)^8+22987125)/x^3-546875/x^7)

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maxima [B]  time = 0.37, size = 179, normalized size = 6.39 \begin {gather*} \frac {x^{8} + 56 \, x^{7} + 1332 \, x^{6} + 2 \, {\left (256 \, {\left (e^{5} + 3\right )} \log \relax (2)^{8} + 63805\right )} x^{4} + 17248 \, x^{5} + 56 \, {\left (256 \, {\left (e^{5} + 3\right )} \log \relax (2)^{8} + 8757\right )} x^{3} + 16 \, {\left (8768 \, {\left (e^{5} + 3\right )} \log \relax (2)^{8} + 27517\right )} x^{2} + 56 \, {\left (8704 \, {\left (e^{5} + 3\right )} \log \relax (2)^{8} - 53081\right )} x - \frac {5 \, {\left (56 \, {\left (8704 \, {\left (e^{5} + 3\right )} \log \relax (2)^{8} - 53081\right )} x^{7} - 80 \, {\left (8768 \, {\left (e^{5} + 3\right )} \log \relax (2)^{8} + 27517\right )} x^{6} + 1400 \, {\left (256 \, {\left (e^{5} + 3\right )} \log \relax (2)^{8} + 8757\right )} x^{5} - 250 \, {\left (256 \, {\left (e^{5} + 3\right )} \log \relax (2)^{8} + 63805\right )} x^{4} + 10780000 \, x^{3} - 4162500 \, x^{2} + 875000 \, x - 78125\right )}}{x^{8}}}{196608 \, \log \relax (2)^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/196608*(256*((8*x^12+168*x^11+1096*x^10+1904*x^9+9520*x^7-27400*x^6+21000*x^5-5000*x^4)*exp(5)+24*
x^12+504*x^11+3288*x^10+5712*x^9+28560*x^7-82200*x^6+63000*x^5-15000*x^4)*log(2)^8+8*x^16+392*x^15+7992*x^14+8
6240*x^13+510440*x^12+1471176*x^11+880544*x^10-2972536*x^9-14862680*x^7-22013600*x^6+183897000*x^5-319025000*x
^4+269500000*x^3-124875000*x^2+30625000*x-3125000)/x^9/log(2)^16,x, algorithm="maxima")

[Out]

1/196608*(x^8 + 56*x^7 + 1332*x^6 + 2*(256*(e^5 + 3)*log(2)^8 + 63805)*x^4 + 17248*x^5 + 56*(256*(e^5 + 3)*log
(2)^8 + 8757)*x^3 + 16*(8768*(e^5 + 3)*log(2)^8 + 27517)*x^2 + 56*(8704*(e^5 + 3)*log(2)^8 - 53081)*x - 5*(56*
(8704*(e^5 + 3)*log(2)^8 - 53081)*x^7 - 80*(8768*(e^5 + 3)*log(2)^8 + 27517)*x^6 + 1400*(256*(e^5 + 3)*log(2)^
8 + 8757)*x^5 - 250*(256*(e^5 + 3)*log(2)^8 + 63805)*x^4 + 10780000*x^3 - 4162500*x^2 + 875000*x - 78125)/x^8)
/log(2)^16

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mupad [B]  time = 0.25, size = 241, normalized size = 8.61 \begin {gather*} \frac {539\,x^5}{6144\,{\ln \relax (2)}^{16}}+\frac {111\,x^6}{16384\,{\ln \relax (2)}^{16}}+\frac {7\,x^7}{24576\,{\ln \relax (2)}^{16}}+\frac {x^8}{196608\,{\ln \relax (2)}^{16}}+\frac {x^4\,\left (256\,{\mathrm {e}}^5\,{\ln \relax (2)}^8+768\,{\ln \relax (2)}^8+63805\right )}{98304\,{\ln \relax (2)}^{16}}+\frac {x^3\,\left (5376\,{\mathrm {e}}^5\,{\ln \relax (2)}^8+16128\,{\ln \relax (2)}^8+183897\right )}{73728\,{\ln \relax (2)}^{16}}+\frac {x^2\,\left (35072\,{\mathrm {e}}^5\,{\ln \relax (2)}^8+105216\,{\ln \relax (2)}^8+110068\right )}{49152\,{\ln \relax (2)}^{16}}+\frac {x\,\left (60928\,{\mathrm {e}}^5\,{\ln \relax (2)}^8+182784\,{\ln \relax (2)}^8-371567\right )}{24576\,{\ln \relax (2)}^{16}}-\frac {\left (304640\,{\mathrm {e}}^5\,{\ln \relax (2)}^8+913920\,{\ln \relax (2)}^8-1857835\right )\,x^7+\left (-438400\,{\mathrm {e}}^5\,{\ln \relax (2)}^8-1315200\,{\ln \relax (2)}^8-1375850\right )\,x^6+\left (224000\,{\mathrm {e}}^5\,{\ln \relax (2)}^8+672000\,{\ln \relax (2)}^8+7662375\right )\,x^5+\left (-40000\,{\mathrm {e}}^5\,{\ln \relax (2)}^8-120000\,{\ln \relax (2)}^8-\frac {39878125}{4}\right )\,x^4+6737500\,x^3-\frac {5203125\,x^2}{2}+546875\,x-\frac {390625}{8}}{24576\,x^8\,{\ln \relax (2)}^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3828125*x)/24576 + (log(2)^8*(63000*x^5 - 15000*x^4 - 82200*x^6 + 28560*x^7 + 5712*x^9 + 3288*x^10 + 504
*x^11 + 24*x^12 + exp(5)*(21000*x^5 - 5000*x^4 - 27400*x^6 + 9520*x^7 + 1904*x^9 + 1096*x^10 + 168*x^11 + 8*x^
12)))/768 - (5203125*x^2)/8192 + (8421875*x^3)/6144 - (39878125*x^4)/24576 + (7662375*x^5)/8192 - (687925*x^6)
/6144 - (1857835*x^7)/24576 - (371567*x^9)/24576 + (27517*x^10)/6144 + (61299*x^11)/8192 + (63805*x^12)/24576
+ (2695*x^13)/6144 + (333*x^14)/8192 + (49*x^15)/24576 + x^16/24576 - 390625/24576)/(x^9*log(2)^16),x)

[Out]

(539*x^5)/(6144*log(2)^16) + (111*x^6)/(16384*log(2)^16) + (7*x^7)/(24576*log(2)^16) + x^8/(196608*log(2)^16)
+ (x^4*(256*exp(5)*log(2)^8 + 768*log(2)^8 + 63805))/(98304*log(2)^16) + (x^3*(5376*exp(5)*log(2)^8 + 16128*lo
g(2)^8 + 183897))/(73728*log(2)^16) + (x^2*(35072*exp(5)*log(2)^8 + 105216*log(2)^8 + 110068))/(49152*log(2)^1
6) + (x*(60928*exp(5)*log(2)^8 + 182784*log(2)^8 - 371567))/(24576*log(2)^16) - (546875*x + x^7*(304640*exp(5)
*log(2)^8 + 913920*log(2)^8 - 1857835) - x^6*(438400*exp(5)*log(2)^8 + 1315200*log(2)^8 + 1375850) + x^5*(2240
00*exp(5)*log(2)^8 + 672000*log(2)^8 + 7662375) - x^4*(40000*exp(5)*log(2)^8 + 120000*log(2)^8 + 39878125/4) -
(5203125*x^2)/2 + 6737500*x^3 - 390625/8)/(24576*x^8*log(2)^16)

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sympy [B]  time = 15.76, size = 226, normalized size = 8.07 \begin {gather*} \frac {\frac {x^{8}}{8} + 7 x^{7} + \frac {333 x^{6}}{2} + 2156 x^{5} + x^{4} \left (192 \log {\relax (2 )}^{8} + 64 e^{5} \log {\relax (2 )}^{8} + \frac {63805}{4}\right ) + x^{3} \left (5376 \log {\relax (2 )}^{8} + 1792 e^{5} \log {\relax (2 )}^{8} + 61299\right ) + x^{2} \left (52608 \log {\relax (2 )}^{8} + 55034 + 17536 e^{5} \log {\relax (2 )}^{8}\right ) + x \left (-371567 + 182784 \log {\relax (2 )}^{8} + 60928 e^{5} \log {\relax (2 )}^{8}\right ) + \frac {x^{7} \left (- 2437120 e^{5} \log {\relax (2 )}^{8} - 7311360 \log {\relax (2 )}^{8} + 14862680\right ) + x^{6} \left (10521600 \log {\relax (2 )}^{8} + 11006800 + 3507200 e^{5} \log {\relax (2 )}^{8}\right ) + x^{5} \left (-61299000 - 1792000 e^{5} \log {\relax (2 )}^{8} - 5376000 \log {\relax (2 )}^{8}\right ) + x^{4} \left (960000 \log {\relax (2 )}^{8} + 320000 e^{5} \log {\relax (2 )}^{8} + 79756250\right ) - 53900000 x^{3} + 20812500 x^{2} - 4375000 x + 390625}{8 x^{8}}}{24576 \log {\relax (2 )}^{16}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/196608*(256*((8*x**12+168*x**11+1096*x**10+1904*x**9+9520*x**7-27400*x**6+21000*x**5-5000*x**4)*ex
p(5)+24*x**12+504*x**11+3288*x**10+5712*x**9+28560*x**7-82200*x**6+63000*x**5-15000*x**4)*ln(2)**8+8*x**16+392
*x**15+7992*x**14+86240*x**13+510440*x**12+1471176*x**11+880544*x**10-2972536*x**9-14862680*x**7-22013600*x**6
[phone]*x**5-319025000*x**4+269500000*x**3-124875000*x**2+30625000*x-3125000)/x**9/ln(2)**16,x)

[Out]

(x**8/8 + 7*x**7 + 333*x**6/2 + 2156*x**5 + x**4*(192*log(2)**8 + 64*exp(5)*log(2)**8 + 63805/4) + x**3*(5376*
log(2)**8 + 1792*exp(5)*log(2)**8 + 61299) + x**2*(52608*log(2)**8 + 55034 + 17536*exp(5)*log(2)**8) + x*(-371
567 + 182784*log(2)**8 + 60928*exp(5)*log(2)**8) + (x**7*(-2437120*exp(5)*log(2)**8 - 7311360*log(2)**8 + 1486
2680) + x**6*(10521600*log(2)**8 + 11006800 + 3507200*exp(5)*log(2)**8) + x**5*(-61299000 - 1792000*exp(5)*log
(2)**8 - 5376000*log(2)**8) + x**4*(960000*log(2)**8 + 320000*exp(5)*log(2)**8 + 79756250) - 53900000*x**3 + 2
0812500*x**2 - 4375000*x + 390625)/(8*x**8))/(24576*log(2)**16)

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