3.89.26 \(\int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+(-144 x^2+384 x^3-576 x^5+336 x^6) \log (2)+(-576 x+2304 x^3-1728 x^5) \log ^2(2)+(-768-3072 x+6144 x^3+3840 x^4) \log ^3(2)+(-3072-9216 x-9216 x^2-3072 x^3) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+(-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}) \log (2)+(-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}) \log ^2(2)+(-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}) \log ^3(2)+(-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}) \log ^4(2)+(57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}) \log ^5(2)+(114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}) \log ^6(2)+(131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9) \log ^7(2)+(65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8) \log ^8(2)} \, dx\)

Optimal. Leaf size=22 \[ \frac {3}{-1+\left (-x+x^2-4 (1+x) \log (2)\right )^4} \]

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Rubi [B]  time = 1.22, antiderivative size = 101, normalized size of antiderivative = 4.59, number of steps used = 5, number of rules used = 3, integrand size = 587, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {2074, 629, 1588} \begin {gather*} -\frac {3+\log (4096)}{4 (1+\log (16)) \left (-x^2+x (1+\log (16))+1+\log (16)\right )}-\frac {3}{4 \left (x^2-x (1+\log (16))+1-4 \log (2)\right )}-\frac {3}{2 \left (x^4-2 x^3 (1+\log (16))+x^2 \left (1+16 \log ^2(2)\right )+8 x \log (2) (1+\log (16))+1+16 \log ^2(2)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-12*x^3 + 60*x^4 - 108*x^5 + 84*x^6 - 24*x^7 + (-144*x^2 + 384*x^3 - 576*x^5 + 336*x^6)*Log[2] + (-576*x
+ 2304*x^3 - 1728*x^5)*Log[2]^2 + (-768 - 3072*x + 6144*x^3 + 3840*x^4)*Log[2]^3 + (-3072 - 9216*x - 9216*x^2
- 3072*x^3)*Log[2]^4)/(1 - 2*x^4 + 8*x^5 - 12*x^6 + 8*x^7 - x^8 - 8*x^9 + 28*x^10 - 56*x^11 + 70*x^12 - 56*x^1
3 + 28*x^14 - 8*x^15 + x^16 + (-32*x^3 + 64*x^4 - 64*x^6 + 64*x^7 - 192*x^8 + 448*x^9 - 448*x^10 + 448*x^12 -
448*x^13 + 192*x^14 - 32*x^15)*Log[2] + (-192*x^2 + 384*x^4 + 256*x^6 - 1792*x^7 + 1792*x^8 + 1792*x^9 - 4480*
x^10 + 1792*x^11 + 1792*x^12 - 1792*x^13 + 448*x^14)*Log[2]^2 + (-512*x - 1024*x^2 + 1024*x^4 + 4096*x^5 - 716
8*x^6 - 7168*x^7 + 21504*x^8 - 21504*x^10 + 7168*x^11 + 7168*x^12 - 3584*x^13)*Log[2]^3 + (-512 - 2048*x - 307
2*x^2 - 2048*x^3 + 17408*x^4 - 71680*x^6 + 107520*x^8 - 71680*x^10 + 17920*x^12)*Log[2]^4 + (57344*x^3 + 11468
8*x^4 - 114688*x^5 - 344064*x^6 + 344064*x^8 + 114688*x^9 - 114688*x^10 - 57344*x^11)*Log[2]^5 + (114688*x^2 +
458752*x^3 + 458752*x^4 - 458752*x^5 - 1146880*x^6 - 458752*x^7 + 458752*x^8 + 458752*x^9 + 114688*x^10)*Log[
2]^6 + (131072*x + 786432*x^2 + 1835008*x^3 + 1835008*x^4 - 1835008*x^6 - 1835008*x^7 - 786432*x^8 - 131072*x^
9)*Log[2]^7 + (65536 + 524288*x + 1835008*x^2 + 3670016*x^3 + 4587520*x^4 + 3670016*x^5 + 1835008*x^6 + 524288
*x^7 + 65536*x^8)*Log[2]^8),x]

[Out]

-3/(4*(1 + x^2 - 4*Log[2] - x*(1 + Log[16]))) - 3/(2*(1 + x^4 + 16*Log[2]^2 + x^2*(1 + 16*Log[2]^2) - 2*x^3*(1
+ Log[16]) + 8*x*Log[2]*(1 + Log[16]))) - (3 + Log[4096])/(4*(1 + Log[16])*(1 - x^2 + Log[16] + x*(1 + Log[16
])))

Rule 629

Int[((d_) + (e_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Simp[(d*(a + b*x + c*x^2)^(p +
1))/(b*(p + 1)), x] /; FreeQ[{a, b, c, d, e, p}, x] && EqQ[2*c*d - b*e, 0] && NeQ[p, -1]

Rule 1588

Int[(Pp_)*(Qq_)^(m_.), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x]}, Simp[(Coeff[Pp, x, p]*x^(p - q
+ 1)*Qq^(m + 1))/((p + m*q + 1)*Coeff[Qq, x, q]), x] /; NeQ[p + m*q + 1, 0] && EqQ[(p + m*q + 1)*Coeff[Qq, x,
q]*Pp, Coeff[Pp, x, p]*x^(p - q)*((p - q + 1)*Qq + (m + 1)*x*D[Qq, x])]] /; FreeQ[m, x] && PolyQ[Pp, x] && Pol
yQ[Qq, x] && NeQ[m, -1]

Rule 2074

Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /;  !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {3 (-1+2 x-4 \log (2))}{4 \left (1+x^2-4 \log (2)-x (1+\log (16))\right )^2}+\frac {3 \left (2 x^3+16 \log ^2(2)+x \left (1+16 \log ^2(2)\right )+\log (16)-3 x^2 (1+\log (16))\right )}{\left (1+x^4+16 \log ^2(2)+x^2 \left (1+16 \log ^2(2)\right )-2 x^3 (1+\log (16))+8 x \log (2) (1+\log (16))\right )^2}+\frac {3-6 x+\log (4096)}{4 \left (1-x^2+\log (16)+x (1+\log (16))\right )^2}\right ) \, dx\\ &=\frac {1}{4} \int \frac {3-6 x+\log (4096)}{\left (1-x^2+\log (16)+x (1+\log (16))\right )^2} \, dx+\frac {3}{4} \int \frac {-1+2 x-4 \log (2)}{\left (1+x^2-4 \log (2)+x (-1-\log (16))\right )^2} \, dx+3 \int \frac {2 x^3+16 \log ^2(2)+x \left (1+16 \log ^2(2)\right )+\log (16)-3 x^2 (1+\log (16))}{\left (1+x^4+16 \log ^2(2)+x^2 \left (1+16 \log ^2(2)\right )-2 x^3 (1+\log (16))+8 x \log (2) (1+\log (16))\right )^2} \, dx\\ &=-\frac {3}{4 \left (1+x^2-4 \log (2)-x (1+\log (16))\right )}-\frac {3}{2 \left (1+x^4+16 \log ^2(2)+x^2 \left (1+16 \log ^2(2)\right )-2 x^3 (1+\log (16))+8 x \log (2) (1+\log (16))\right )}-\frac {3+\log (4096)}{4 (1+\log (16)) \left (1-x^2+\log (16)+x (1+\log (16))\right )}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 95.15, size = 19960, normalized size = 907.27 \begin {gather*} \text {Result too large to show} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-12*x^3 + 60*x^4 - 108*x^5 + 84*x^6 - 24*x^7 + (-144*x^2 + 384*x^3 - 576*x^5 + 336*x^6)*Log[2] + (-
576*x + 2304*x^3 - 1728*x^5)*Log[2]^2 + (-768 - 3072*x + 6144*x^3 + 3840*x^4)*Log[2]^3 + (-3072 - 9216*x - 921
6*x^2 - 3072*x^3)*Log[2]^4)/(1 - 2*x^4 + 8*x^5 - 12*x^6 + 8*x^7 - x^8 - 8*x^9 + 28*x^10 - 56*x^11 + 70*x^12 -
56*x^13 + 28*x^14 - 8*x^15 + x^16 + (-32*x^3 + 64*x^4 - 64*x^6 + 64*x^7 - 192*x^8 + 448*x^9 - 448*x^10 + 448*x
^12 - 448*x^13 + 192*x^14 - 32*x^15)*Log[2] + (-192*x^2 + 384*x^4 + 256*x^6 - 1792*x^7 + 1792*x^8 + 1792*x^9 -
4480*x^10 + 1792*x^11 + 1792*x^12 - 1792*x^13 + 448*x^14)*Log[2]^2 + (-512*x - 1024*x^2 + 1024*x^4 + 4096*x^5
- 7168*x^6 - 7168*x^7 + 21504*x^8 - 21504*x^10 + 7168*x^11 + 7168*x^12 - 3584*x^13)*Log[2]^3 + (-512 - 2048*x
- 3072*x^2 - 2048*x^3 + 17408*x^4 - 71680*x^6 + 107520*x^8 - 71680*x^10 + 17920*x^12)*Log[2]^4 + (57344*x^3 +
114688*x^4 - 114688*x^5 - 344064*x^6 + 344064*x^8 + 114688*x^9 - 114688*x^10 - 57344*x^11)*Log[2]^5 + (114688
*x^2 + 458752*x^3 + 458752*x^4 - 458752*x^5 - 1146880*x^6 - 458752*x^7 + 458752*x^8 + 458752*x^9 + 114688*x^10
)*Log[2]^6 + (131072*x + 786432*x^2 + 1835008*x^3 + 1835008*x^4 - 1835008*x^6 - 1835008*x^7 - 786432*x^8 - 131
072*x^9)*Log[2]^7 + (65536 + 524288*x + 1835008*x^2 + 3670016*x^3 + 4587520*x^4 + 3670016*x^5 + 1835008*x^6 +
524288*x^7 + 65536*x^8)*Log[2]^8),x]

[Out]

Result too large to show

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fricas [B]  time = 0.48, size = 115, normalized size = 5.23 \begin {gather*} \frac {3}{x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + 256 \, {\left (x^{4} + 4 \, x^{3} + 6 \, x^{2} + 4 \, x + 1\right )} \log \relax (2)^{4} + x^{4} - 256 \, {\left (x^{5} + 2 \, x^{4} - 2 \, x^{2} - x\right )} \log \relax (2)^{3} + 96 \, {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} \log \relax (2)^{2} - 16 \, {\left (x^{7} - 2 \, x^{6} + 2 \, x^{4} - x^{3}\right )} \log \relax (2) - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3072*x^3-9216*x^2-9216*x-3072)*log(2)^4+(3840*x^4+6144*x^3-3072*x-768)*log(2)^3+(-1728*x^5+2304*x
^3-576*x)*log(2)^2+(336*x^6-576*x^5+384*x^3-144*x^2)*log(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+5
24288*x^7+1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288*x+65536)*log(2)^8+(-131072*x^9-78
6432*x^8-1835008*x^7-1835008*x^6+1835008*x^4+1835008*x^3+786432*x^2+131072*x)*log(2)^7+(114688*x^10+458752*x^9
+458752*x^8-458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2)*log(2)^6+(-57344*x^11-114688*x
^10+114688*x^9+344064*x^8-344064*x^6-114688*x^5+114688*x^4+57344*x^3)*log(2)^5+(17920*x^12-71680*x^10+107520*x
^8-71680*x^6+17408*x^4-2048*x^3-3072*x^2-2048*x-512)*log(2)^4+(-3584*x^13+7168*x^12+7168*x^11-21504*x^10+21504
*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-1024*x^2-512*x)*log(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480
*x^10+1792*x^9+1792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*log(2)^2+(-32*x^15+192*x^14-448*x^13+448*x^12-448*x^
10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3)*log(2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x
^9-x^8+8*x^7-12*x^6+8*x^5-2*x^4+1),x, algorithm="fricas")

[Out]

3/(x^8 - 4*x^7 + 6*x^6 - 4*x^5 + 256*(x^4 + 4*x^3 + 6*x^2 + 4*x + 1)*log(2)^4 + x^4 - 256*(x^5 + 2*x^4 - 2*x^2
- x)*log(2)^3 + 96*(x^6 - 2*x^4 + x^2)*log(2)^2 - 16*(x^7 - 2*x^6 + 2*x^4 - x^3)*log(2) - 1)

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3072*x^3-9216*x^2-9216*x-3072)*log(2)^4+(3840*x^4+6144*x^3-3072*x-768)*log(2)^3+(-1728*x^5+2304*x
^3-576*x)*log(2)^2+(336*x^6-576*x^5+384*x^3-144*x^2)*log(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+5
24288*x^7+1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288*x+65536)*log(2)^8+(-131072*x^9-78
6432*x^8-1835008*x^7-1835008*x^6+1835008*x^4+1835008*x^3+786432*x^2+131072*x)*log(2)^7+(114688*x^10+458752*x^9
+458752*x^8-458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2)*log(2)^6+(-57344*x^11-114688*x
^10+114688*x^9+344064*x^8-344064*x^6-114688*x^5+114688*x^4+57344*x^3)*log(2)^5+(17920*x^12-71680*x^10+107520*x
^8-71680*x^6+17408*x^4-2048*x^3-3072*x^2-2048*x-512)*log(2)^4+(-3584*x^13+7168*x^12+7168*x^11-21504*x^10+21504
*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-1024*x^2-512*x)*log(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480
*x^10+1792*x^9+1792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*log(2)^2+(-32*x^15+192*x^14-448*x^13+448*x^12-448*x^
10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3)*log(2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x
^9-x^8+8*x^7-12*x^6+8*x^5-2*x^4+1),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choi
ce was done

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maple [B]  time = 1.42, size = 157, normalized size = 7.14

method	result	size
gosper	\(\frac {3}{256 \ln \relax (2)^{4} x^{4}-256 x^{5} \ln \relax (2)^{3}+96 x^{6} \ln \relax (2)^{2}-16 x^{7} \ln \relax (2)+x^{8}+1024 x^{3} \ln \relax (2)^{4}-512 x^{4} \ln \relax (2)^{3}+32 x^{6} \ln \relax (2)-4 x^{7}+1536 x^{2} \ln \relax (2)^{4}-192 x^{4} \ln \relax (2)^{2}+6 x^{6}+1024 x \ln \relax (2)^{4}+512 x^{2} \ln \relax (2)^{3}-32 x^{4} \ln \relax (2)-4 x^{5}+256 \ln \relax (2)^{4}+256 x \ln \relax (2)^{3}+96 x^{2} \ln \relax (2)^{2}+16 x^{3} \ln \relax (2)+x^{4}-1}\)	\(157\)
default	\(-\frac {3}{32 \left (x^{2} \ln \relax (2)^{2}-\frac {x^{3} \ln \relax (2)}{2}+\frac {x^{4}}{16}+2 x \ln \relax (2)^{2}-\frac {x^{3}}{8}+\ln \relax (2)^{2}+\frac {x \ln \relax (2)}{2}+\frac {x^{2}}{16}+\frac {1}{16}\right )}+\frac {-3+\frac {3 \left (1+4 \ln \relax (2)\right ) \left (-4 \ln \relax (2)-1\right )}{4}-12 \ln \relax (2)}{\left (-16 \ln \relax (2)^{2}-24 \ln \relax (2)-5\right ) \left (-4 x \ln \relax (2)+x^{2}-4 \ln \relax (2)-x -1\right )}+\frac {-3+\frac {3 \left (-4 \ln \relax (2)-1\right )^{2}}{4}+12 \ln \relax (2)}{\left (-16 \ln \relax (2)^{2}-24 \ln \relax (2)+3\right ) \left (-4 x \ln \relax (2)+x^{2}-4 \ln \relax (2)-x +1\right )}\)	\(157\)
norman	\(\frac {3}{256 \ln \relax (2)^{4} x^{4}-256 x^{5} \ln \relax (2)^{3}+96 x^{6} \ln \relax (2)^{2}-16 x^{7} \ln \relax (2)+x^{8}+1024 x^{3} \ln \relax (2)^{4}-512 x^{4} \ln \relax (2)^{3}+32 x^{6} \ln \relax (2)-4 x^{7}+1536 x^{2} \ln \relax (2)^{4}-192 x^{4} \ln \relax (2)^{2}+6 x^{6}+1024 x \ln \relax (2)^{4}+512 x^{2} \ln \relax (2)^{3}-32 x^{4} \ln \relax (2)-4 x^{5}+256 \ln \relax (2)^{4}+256 x \ln \relax (2)^{3}+96 x^{2} \ln \relax (2)^{2}+16 x^{3} \ln \relax (2)+x^{4}-1}\)	\(157\)
risch	\(\frac {3}{256 \left (\ln \relax (2)^{4} x^{4}-x^{5} \ln \relax (2)^{3}+\frac {3 x^{6} \ln \relax (2)^{2}}{8}-\frac {x^{7} \ln \relax (2)}{16}+\frac {x^{8}}{256}+4 x^{3} \ln \relax (2)^{4}-2 x^{4} \ln \relax (2)^{3}+\frac {x^{6} \ln \relax (2)}{8}-\frac {x^{7}}{64}+6 x^{2} \ln \relax (2)^{4}-\frac {3 x^{4} \ln \relax (2)^{2}}{4}+\frac {3 x^{6}}{128}+4 x \ln \relax (2)^{4}+2 x^{2} \ln \relax (2)^{3}-\frac {x^{4} \ln \relax (2)}{8}-\frac {x^{5}}{64}+\ln \relax (2)^{4}+x \ln \relax (2)^{3}+\frac {3 x^{2} \ln \relax (2)^{2}}{8}+\frac {x^{3} \ln \relax (2)}{16}+\frac {x^{4}}{256}-\frac {1}{256}\right )}\)	\(157\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-3072*x^3-9216*x^2-9216*x-3072)*ln(2)^4+(3840*x^4+6144*x^3-3072*x-768)*ln(2)^3+(-1728*x^5+2304*x^3-576*x
)*ln(2)^2+(336*x^6-576*x^5+384*x^3-144*x^2)*ln(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+524288*x^7+
1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288*x+65536)*ln(2)^8+(-131072*x^9-786432*x^8-18
35008*x^7-1835008*x^6+1835008*x^4+1835008*x^3+786432*x^2+131072*x)*ln(2)^7+(114688*x^10+458752*x^9+458752*x^8-
458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2)*ln(2)^6+(-57344*x^11-114688*x^10+114688*x^
9+344064*x^8-344064*x^6-114688*x^5+114688*x^4+57344*x^3)*ln(2)^5+(17920*x^12-71680*x^10+107520*x^8-71680*x^6+1
7408*x^4-2048*x^3-3072*x^2-2048*x-512)*ln(2)^4+(-3584*x^13+7168*x^12+7168*x^11-21504*x^10+21504*x^8-7168*x^7-7
168*x^6+4096*x^5+1024*x^4-1024*x^2-512*x)*ln(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480*x^10+1792*x^9+1
792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*ln(2)^2+(-32*x^15+192*x^14-448*x^13+448*x^12-448*x^10+448*x^9-192*x^
8+64*x^7-64*x^6+64*x^4-32*x^3)*ln(2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x^9-x^8+8*x^7-12*x^
6+8*x^5-2*x^4+1),x,method=_RETURNVERBOSE)

[Out]

3/(256*ln(2)^4*x^4-256*x^5*ln(2)^3+96*x^6*ln(2)^2-16*x^7*ln(2)+x^8+1024*x^3*ln(2)^4-512*x^4*ln(2)^3+32*x^6*ln(
2)-4*x^7+1536*x^2*ln(2)^4-192*x^4*ln(2)^2+6*x^6+1024*x*ln(2)^4+512*x^2*ln(2)^3-32*x^4*ln(2)-4*x^5+256*ln(2)^4+
256*x*ln(2)^3+96*x^2*ln(2)^2+16*x^3*ln(2)+x^4-1)

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maxima [B]  time = 0.38, size = 136, normalized size = 6.18 \begin {gather*} \frac {3}{x^{8} - 4 \, x^{7} {\left (4 \, \log \relax (2) + 1\right )} + 2 \, {\left (48 \, \log \relax (2)^{2} + 16 \, \log \relax (2) + 3\right )} x^{6} - 4 \, {\left (64 \, \log \relax (2)^{3} + 1\right )} x^{5} + {\left (256 \, \log \relax (2)^{4} - 512 \, \log \relax (2)^{3} - 192 \, \log \relax (2)^{2} - 32 \, \log \relax (2) + 1\right )} x^{4} + 16 \, {\left (64 \, \log \relax (2)^{4} + \log \relax (2)\right )} x^{3} + 256 \, \log \relax (2)^{4} + 32 \, {\left (48 \, \log \relax (2)^{4} + 16 \, \log \relax (2)^{3} + 3 \, \log \relax (2)^{2}\right )} x^{2} + 256 \, {\left (4 \, \log \relax (2)^{4} + \log \relax (2)^{3}\right )} x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3072*x^3-9216*x^2-9216*x-3072)*log(2)^4+(3840*x^4+6144*x^3-3072*x-768)*log(2)^3+(-1728*x^5+2304*x
^3-576*x)*log(2)^2+(336*x^6-576*x^5+384*x^3-144*x^2)*log(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+5
24288*x^7+1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288*x+65536)*log(2)^8+(-131072*x^9-78
6432*x^8-1835008*x^7-1835008*x^6+1835008*x^4+1835008*x^3+786432*x^2+131072*x)*log(2)^7+(114688*x^10+458752*x^9
+458752*x^8-458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2)*log(2)^6+(-57344*x^11-114688*x
^10+114688*x^9+344064*x^8-344064*x^6-114688*x^5+114688*x^4+57344*x^3)*log(2)^5+(17920*x^12-71680*x^10+107520*x
^8-71680*x^6+17408*x^4-2048*x^3-3072*x^2-2048*x-512)*log(2)^4+(-3584*x^13+7168*x^12+7168*x^11-21504*x^10+21504
*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-1024*x^2-512*x)*log(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480
*x^10+1792*x^9+1792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*log(2)^2+(-32*x^15+192*x^14-448*x^13+448*x^12-448*x^
10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3)*log(2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x
^9-x^8+8*x^7-12*x^6+8*x^5-2*x^4+1),x, algorithm="maxima")

[Out]

3/(x^8 - 4*x^7*(4*log(2) + 1) + 2*(48*log(2)^2 + 16*log(2) + 3)*x^6 - 4*(64*log(2)^3 + 1)*x^5 + (256*log(2)^4
- 512*log(2)^3 - 192*log(2)^2 - 32*log(2) + 1)*x^4 + 16*(64*log(2)^4 + log(2))*x^3 + 256*log(2)^4 + 32*(48*log
(2)^4 + 16*log(2)^3 + 3*log(2)^2)*x^2 + 256*(4*log(2)^4 + log(2)^3)*x - 1)

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mupad [F(-1)]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \text {Hanged} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(2)*(144*x^2 - 384*x^3 + 576*x^5 - 336*x^6) + log(2)^2*(576*x - 2304*x^3 + 1728*x^5) + log(2)^3*(3072
*x - 6144*x^3 - 3840*x^4 + 768) + log(2)^4*(9216*x + 9216*x^2 + 3072*x^3 + 3072) + 12*x^3 - 60*x^4 + 108*x^5 -
84*x^6 + 24*x^7)/(log(2)^5*(57344*x^3 + 114688*x^4 - 114688*x^5 - 344064*x^6 + 344064*x^8 + 114688*x^9 - 1146
88*x^10 - 57344*x^11) + log(2)^6*(114688*x^2 + 458752*x^3 + 458752*x^4 - 458752*x^5 - 1146880*x^6 - 458752*x^7
+ 458752*x^8 + 458752*x^9 + 114688*x^10) - log(2)*(32*x^3 - 64*x^4 + 64*x^6 - 64*x^7 + 192*x^8 - 448*x^9 + 44
8*x^10 - 448*x^12 + 448*x^13 - 192*x^14 + 32*x^15) - log(2)^3*(512*x + 1024*x^2 - 1024*x^4 - 4096*x^5 + 7168*x
^6 + 7168*x^7 - 21504*x^8 + 21504*x^10 - 7168*x^11 - 7168*x^12 + 3584*x^13) - 2*x^4 + 8*x^5 - 12*x^6 + 8*x^7 -
x^8 - 8*x^9 + 28*x^10 - 56*x^11 + 70*x^12 - 56*x^13 + 28*x^14 - 8*x^15 + x^16 - log(2)^4*(2048*x + 3072*x^2 +
2048*x^3 - 17408*x^4 + 71680*x^6 - 107520*x^8 + 71680*x^10 - 17920*x^12 + 512) + log(2)^7*(131072*x + 786432*
x^2 + 1835008*x^3 + 1835008*x^4 - 1835008*x^6 - 1835008*x^7 - 786432*x^8 - 131072*x^9) + log(2)^8*(524288*x +
1835008*x^2 + 3670016*x^3 + 4587520*x^4 + 3670016*x^5 + 1835008*x^6 + 524288*x^7 + 65536*x^8 + 65536) + log(2)
^2*(384*x^4 - 192*x^2 + 256*x^6 - 1792*x^7 + 1792*x^8 + 1792*x^9 - 4480*x^10 + 1792*x^11 + 1792*x^12 - 1792*x^
13 + 448*x^14) + 1),x)

[Out]

\text{Hanged}

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sympy [B]  time = 19.63, size = 139, normalized size = 6.32 \begin {gather*} \frac {3}{x^{8} + x^{7} \left (- 16 \log {\relax (2 )} - 4\right ) + x^{6} \left (6 + 32 \log {\relax (2 )} + 96 \log {\relax (2 )}^{2}\right ) + x^{5} \left (- 256 \log {\relax (2 )}^{3} - 4\right ) + x^{4} \left (- 512 \log {\relax (2 )}^{3} - 192 \log {\relax (2 )}^{2} - 32 \log {\relax (2 )} + 1 + 256 \log {\relax (2 )}^{4}\right ) + x^{3} \left (16 \log {\relax (2 )} + 1024 \log {\relax (2 )}^{4}\right ) + x^{2} \left (96 \log {\relax (2 )}^{2} + 512 \log {\relax (2 )}^{3} + 1536 \log {\relax (2 )}^{4}\right ) + x \left (256 \log {\relax (2 )}^{3} + 1024 \log {\relax (2 )}^{4}\right ) - 1 + 256 \log {\relax (2 )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-3072*x**3-9216*x**2-9216*x-3072)*ln(2)**4+(3840*x**4+6144*x**3-3072*x-768)*ln(2)**3+(-1728*x**5+2
304*x**3-576*x)*ln(2)**2+(336*x**6-576*x**5+384*x**3-144*x**2)*ln(2)-24*x**7+84*x**6-108*x**5+60*x**4-12*x**3)
/((65536*x**8+524288*x**7+1835008*x**6+3670016*x**5+4587520*x**4+3670016*x**3+1835008*x**2+524288*x+65536)*ln(
2)**8+(-131072*x**9-786432*x**8-1835008*x**7-1835008*x**6+1835008*x**4+1835008*x**3+786432*x**2+131072*x)*ln(2
)**7+(114688*x**10+458752*x**9+458752*x**8-458752*x**7-1146880*x**6-458752*x**5+458752*x**4+458752*x**3+114688
*x**2)*ln(2)**6+(-57344*x**11-114688*x**10+114688*x**9+344064*x**8-344064*x**6-114688*x**5+114688*x**4+57344*x
**3)*ln(2)**5+(17920*x**12-71680*x**10+107520*x**8-71680*x**6+17408*x**4-2048*x**3-3072*x**2-2048*x-512)*ln(2)
**4+(-3584*x**13+7168*x**12+7168*x**11-21504*x**10+21504*x**8-7168*x**7-7168*x**6+4096*x**5+1024*x**4-1024*x**
2-512*x)*ln(2)**3+(448*x**14-1792*x**13+1792*x**12+1792*x**11-4480*x**10+1792*x**9+1792*x**8-1792*x**7+256*x**
6+384*x**4-192*x**2)*ln(2)**2+(-32*x**15+192*x**14-448*x**13+448*x**12-448*x**10+448*x**9-192*x**8+64*x**7-64*
x**6+64*x**4-32*x**3)*ln(2)+x**16-8*x**15+28*x**14-56*x**13+70*x**12-56*x**11+28*x**10-8*x**9-x**8+8*x**7-12*x
**6+8*x**5-2*x**4+1),x)

[Out]

3/(x**8 + x**7*(-16*log(2) - 4) + x**6*(6 + 32*log(2) + 96*log(2)**2) + x**5*(-256*log(2)**3 - 4) + x**4*(-512
*log(2)**3 - 192*log(2)**2 - 32*log(2) + 1 + 256*log(2)**4) + x**3*(16*log(2) + 1024*log(2)**4) + x**2*(96*log
(2)**2 + 512*log(2)**3 + 1536*log(2)**4) + x*(256*log(2)**3 + 1024*log(2)**4) - 1 + 256*log(2)**4)

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