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

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

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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} $$\begin{array}{c}\frac{x^8}{3{\log }^{16}(4)}+\frac{390625}{3x^8{\log }^{16}(4)}+\frac{56x^7}{3{\log }^{16}(4)}-\frac{4375000}{3x^7{\log }^{16}(4)}+\frac{444x^6}{{\log }^{16}(4)}+\frac{6937500}{x^6{\log }^{16}(4)}+\frac{17248x^5}{3{\log }^{16}(4)}-\frac{53900000}{3x^5{\log }^{16}(4)}+\frac{2x^4(63805+3{\log }^8(4)+e^5{\log }^8(4))}{3{\log }^{16}(4)}[phone]\frac{\mathrm{}\mathrm{}+3{\log }^8(4)+e^5{\log }^8(4))}{3x^4{\log }^{16}(4)}+\frac{56x^3(8757+3{\log }^8(4)+e^5{\log }^8(4))}{3{\log }^{16}(4)}-\frac{7000(8757+3{\log }^8(4)+e^5{\log }^8(4))}{3x^3{\log }^{16}(4)}+\frac{4x^2(110068+411{\log }^8(4)+137e^5{\log }^8(4))}{3{\log }^{16}(4)}[phone]\frac{\mathrm{}\mathrm{}+411{\log }^8(4)+137e^5{\log }^8(4))}{3x^2{\log }^{16}(4)}-\frac{56x(53081-102{\log }^8(4)-34e^5{\log }^8(4))}{3{\log }^{16}(4)}[phone]\frac{\mathrm{}\mathrm{}-102{\log }^8(4)-34e^5{\log }^8(4))}{3x{\log }^{16}(4)}\end{array}$$

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

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

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

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 $$\begin{array}{c}\frac{x^{16}+56x^{15}+1332x^{14}+17248x^{13}+127610x^{12}+490392x^{11}+440272x^{10}-2972536x^9+512(3x^{12}+84x^{11}+822x^{10}+2856x^9-14280x^7+20550x^6-10500x^5+1875x^4+(x^{12}+28x^{11}+274x^{10}+952x^9-4760x^7+6850x^6-3500x^5+625x^4)e^5)\log (2{)}^8+14862680x^7+11006800x^6-61299000x^5+79756250x^4-53900000x^3+20812500x^2-4375000x+390625}{196608x^8\log (2{)}^{16}}\end{array}$$

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 $$\begin{array}{c}\frac{512x^4{e}^5\log (2{)}^8+1536x^4\log (2{)}^8+14336x^3{e}^5\log (2{)}^8+43008x^3\log (2{)}^8+140288x^2{e}^5\log (2{)}^8+420864x^2\log (2{)}^8+487424x{e}^5\log (2{)}^8+1462272x\log (2{)}^8+x^8+56x^7+1332x^6+17248x^5+127610x^4+490392x^3+440272x^2-2972536x-\frac{5(487424x^7{e}^5\log (2{)}^8+1462272x^7\log (2{)}^8-701440x^6{e}^5\log (2{)}^8-2104320x^6\log (2{)}^8+358400x^5{e}^5\log (2{)}^8+1075200x^5\log (2{)}^8-64000x^4{e}^5\log (2{)}^8-192000x^4\log (2{)}^8-2972536x^7-2201360x^6+12259800x^5-15951250x^4+10780000x^3-4162500x^2+875000x-78125)}{x^8}}{196608\log (2{)}^{16}}\end{array}$$

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

________________________________________________________________________________________

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

method	result	size
default	$\frac{64{\mathrm{e}}^5\ln (2{)}^8{x}^4+1792{\mathrm{e}}^5\ln (2{)}^8{x}^3+192\ln (2{)}^8{x}^4+17536{\mathrm{e}}^5\ln (2{)}^8{x}^2+5376\ln (2{)}^8{x}^3+60928{\mathrm{e}}^5\ln (2{)}^{8}x+52608\ln (2{)}^8{x}^2+182784x\ln (2{)}^8+\frac{x^8}{8}+7x^7+\frac{333x^6}{2}+2156x^5+\frac{63805x^4}{4}+61299x^3+55034x^2-371567x+\frac{390625}{8x^8}-\frac{-160000{\mathrm{e}}^5\ln (2{)}^8-480000\ln (2{)}^8-39878125}{4x^4}-\frac{6737500}{x^5}+\frac{5203125}{2x^6}-\frac{-876800{\mathrm{e}}^5\ln (2{)}^8-2630400\ln (2{)}^8-2751700}{2x^2}-\frac{304640{\mathrm{e}}^5\ln (2{)}^8+913920\ln (2{)}^8-1857835}{x}-\frac{672000{\mathrm{e}}^5\ln (2{)}^8+2016000\ln (2{)}^8+22987125}{3x^3}-\frac{546875}{x^7}}{24576\ln (2{)}^{16}}$	$226$
gosper	$\frac{390625-4375000x+1462272x^9\ln (2{)}^8+490392x^{11}+127610x^{12}+17248x^{13}+1332x^{14}+x^{16}+56x^{15}+14862680x^7+440272x^{10}-2972536x^9+11006800x^6-61299000x^5+79756250x^4-53900000x^3+20812500x^2-7311360x^7\ln (2{)}^8+420864x^{10}\ln (2{)}^8+512{\mathrm{e}}^5\ln (2{)}^8{x}^{12}+14336{\mathrm{e}}^5\ln (2{)}^8{x}^{11}+10521600\ln (2{)}^8{x}^6-5376000\ln (2{)}^8{x}^5+960000\ln (2{)}^8{x}^4-1792000{\mathrm{e}}^5\ln (2{)}^8{x}^5+3507200{\mathrm{e}}^5\ln (2{)}^8{x}^6+320000{\mathrm{e}}^5\ln (2{)}^8{x}^4+140288{\mathrm{e}}^5\ln (2{)}^8{x}^{10}+487424{\mathrm{e}}^5\ln (2{)}^8{x}^9-2437120{\mathrm{e}}^5\ln (2{)}^8{x}^7+1536\ln (2{)}^8{x}^{12}+43008\ln (2{)}^8{x}^{11}}{196608\ln (2{)}^{16}{x}^8}$	$243$
risch	$\frac{{\mathrm{e}}^5{x}^4}{384\ln (2{)}^8}+\frac{7{\mathrm{e}}^5{x}^3}{96\ln (2{)}^8}+\frac{x^4}{128\ln (2{)}^8}+\frac{137{\mathrm{e}}^5{x}^2}{192\ln (2{)}^8}+\frac{7x^3}{32\ln (2{)}^8}+\frac{119{\mathrm{e}}^{5}x}{48\ln (2{)}^8}+\frac{137x^2}{64\ln (2{)}^8}+\frac{119x}{16\ln (2{)}^8}+\frac{x^8}{196608\ln (2{)}^{16}}+\frac{7x^7}{24576\ln (2{)}^{16}}+\frac{111x^6}{16384\ln (2{)}^{16}}+\frac{539x^5}{6144\ln (2{)}^{16}}+\frac{63805x^4}{98304\ln (2{)}^{16}}+\frac{20433x^3}{8192\ln (2{)}^{16}}+\frac{27517x^2}{12288\ln (2{)}^{16}}-\frac{371567x}{24576\ln (2{)}^{16}}+\frac{(-2437120{\mathrm{e}}^5\ln (2{)}^8-7311360\ln (2{)}^8+14862680)x^7+(3507200{\mathrm{e}}^5\ln (2{)}^8+10521600\ln (2{)}^8+11006800)x^6+(-1792000{\mathrm{e}}^5\ln (2{)}^8-5376000\ln (2{)}^8-61299000)x^5+(320000{\mathrm{e}}^5\ln (2{)}^8+960000\ln (2{)}^8+79756250)x^4-53900000x^3+20812500x^2-4375000x+390625}{196608\ln (2{)}^{16}{x}^8}$	$252$
norman	$\frac{\frac{390625}{196608\ln (2)}-\frac{546875x}{24576\ln (2)}+\frac{1734375x^2}{16384\ln (2)}-\frac{1684375x^3}{6144\ln (2)}+\frac{539x^{13}}{6144\ln (2)}+\frac{111x^{14}}{16384\ln (2)}+\frac{7x^{15}}{24576\ln (2)}+\frac{x^{16}}{196608\ln (2)}-\frac{875(256{\mathrm{e}}^5\ln (2{)}^8+768\ln (2{)}^8+8757)x^5}{24576\ln (2)}+\frac{7(256{\mathrm{e}}^5\ln (2{)}^8+768\ln (2{)}^8+8757)x^{11}}{24576\ln (2)}+\frac{625(256{\mathrm{e}}^5\ln (2{)}^8+768\ln (2{)}^8+63805)x^4}{98304\ln (2)}+\frac{(256{\mathrm{e}}^5\ln (2{)}^8+768\ln (2{)}^8+63805)x^{12}}{98304\ln (2)}-\frac{35(8704{\mathrm{e}}^5\ln (2{)}^8+26112\ln (2{)}^8-53081)x^7}{24576\ln (2)}+\frac{7(8704{\mathrm{e}}^5\ln (2{)}^8+26112\ln (2{)}^8-53081)x^9}{24576\ln (2)}+\frac{25(8768{\mathrm{e}}^5\ln (2{)}^8+26304\ln (2{)}^8+27517)x^6}{12288\ln (2)}+\frac{(8768{\mathrm{e}}^5\ln (2{)}^8+26304\ln (2{)}^8+27517)x^{10}}{12288\ln (2)}}{x^8\ln (2{)}^{15}}$	$277$

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 $$\begin{array}{c}\frac{x^8+56x^7+1332x^6+2(256(e^5+3)\log (2{)}^8+63805)x^4+17248x^5+56(256(e^5+3)\log (2{)}^8+8757)x^3+16(8768(e^5+3)\log (2{)}^8+27517)x^2+56(8704(e^5+3)\log (2{)}^8-53081)x-\frac{5(56(8704(e^5+3)\log (2{)}^8-53081)x^7-80(8768(e^5+3)\log (2{)}^8+27517)x^6+1400(256(e^5+3)\log (2{)}^8+8757)x^5-250(256(e^5+3)\log (2{)}^8+63805)x^4+10780000x^3-4162500x^2+875000x-78125)}{x^8}}{196608\log (2{)}^{16}}\end{array}$$

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 $$\begin{array}{c}\frac{539x^5}{6144{\ln (2)}^{16}}+\frac{111x^6}{16384{\ln (2)}^{16}}+\frac{7x^7}{24576{\ln (2)}^{16}}+\frac{x^8}{196608{\ln (2)}^{16}}+\frac{x^4(256{\mathrm{e}}^5{\ln (2)}^8+768{\ln (2)}^8+63805)}{98304{\ln (2)}^{16}}+\frac{x^3(5376{\mathrm{e}}^5{\ln (2)}^8+16128{\ln (2)}^8+183897)}{73728{\ln (2)}^{16}}+\frac{x^2(35072{\mathrm{e}}^5{\ln (2)}^8+105216{\ln (2)}^8+110068)}{49152{\ln (2)}^{16}}+\frac{x(60928{\mathrm{e}}^5{\ln (2)}^8+182784{\ln (2)}^8-371567)}{24576{\ln (2)}^{16}}-\frac{(304640{\mathrm{e}}^5{\ln (2)}^8+913920{\ln (2)}^8-1857835)x^7+(-438400{\mathrm{e}}^5{\ln (2)}^8-1315200{\ln (2)}^8-1375850)x^6+(224000{\mathrm{e}}^5{\ln (2)}^8+672000{\ln (2)}^8+7662375)x^5+(-40000{\mathrm{e}}^5{\ln (2)}^8-120000{\ln (2)}^8-\frac{39878125}{4})x^4+6737500x^3-\frac{5203125x^2}{2}+546875x-\frac{390625}{8}}{24576x^8{\ln (2)}^{16}}\end{array}$$

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 $$\begin{array}{c}\frac{\frac{x^8}{8}+7x^7+\frac{333x^6}{2}+2156x^5+x^4(192\log {(2)}^8+64e^5\log {(2)}^8+\frac{63805}{4})+x^3(5376\log {(2)}^8+1792e^5\log {(2)}^8+61299)+x^2(52608\log {(2)}^8+55034+17536e^5\log {(2)}^8)+x(-371567+182784\log {(2)}^8+60928e^5\log {(2)}^8)+\frac{x^7(-2437120e^5\log {(2)}^8-7311360\log {(2)}^8+14862680)+x^6(10521600\log {(2)}^8+11006800+3507200e^5\log {(2)}^8)+x^5(-61299000-1792000e^5\log {(2)}^8-5376000\log {(2)}^8)+x^4(960000\log {(2)}^8+320000e^5\log {(2)}^8+79756250)-53900000x^3+20812500x^2-4375000x+390625}{8x^8}}{24576\log {(2)}^{16}}\end{array}$$

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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