3.12.85 \(\int \frac {-4096-9984 x-9600 x^2-4544 x^3-864 x^4+432 x^5+568 x^6+300 x^7+78 x^8+8 x^9+(1024+2560 x+2560 x^2+1280 x^3+256 x^4-128 x^5-160 x^6-80 x^7-20 x^8-2 x^9) \log (2)+(-6144 x-8832 x^2-6208 x^3-1664 x^4+832 x^5+776 x^6+276 x^7+48 x^8+(1536 x+2304 x^2+1664 x^3+448 x^4-224 x^5-208 x^6-72 x^7-12 x^8) \log (2)) \log (5)+(-3072-5440 x-7648 x^2-4128 x^3-528 x^4+444 x^5+402 x^6+120 x^7+(768+1408 x+1984 x^2+1120 x^3+144 x^4-120 x^5-108 x^6-30 x^7) \log (2)) \log ^2(5)+(-3072 x-2880 x^2-1728 x^3-352 x^4+344 x^5+160 x^6+(768 x+768 x^2+448 x^3+96 x^4-96 x^5-40 x^6) \log (2)) \log ^3(5)+(-768-848 x-1256 x^2-460 x^3+210 x^4+120 x^5+(192+224 x+320 x^2+128 x^3-60 x^4-30 x^5) \log (2)) \log ^4(5)+(-384 x-168 x^2+84 x^3+48 x^4+(96 x+48 x^2-24 x^3-12 x^4) \log (2)) \log ^5(5)+(-64-28 x+14 x^2+8 x^3+(16+8 x-4 x^2-2 x^3) \log (2)) \log ^6(5)}{2048+5120 x+6656 x^2+6400 x^3+4864 x^4+2944 x^5+1472 x^6+608 x^7+200 x^8+52 x^9+10 x^{10}+x^{11}+(3072 x+7680 x^2+9216 x^3+7680 x^4+4992 x^5+2496 x^6+960 x^7+288 x^8+60 x^9+6 x^{10}) \log (5)+(1536+3840 x+6144 x^2+7680 x^3+6720 x^4+4128 x^5+1920 x^6+672 x^7+150 x^8+15 x^9) \log ^2(5)+(1536 x+3840 x^2+4480 x^3+3520 x^4+2080 x^5+848 x^6+200 x^7+20 x^8) \log ^3(5)+(384+960 x+1440 x^2+1680 x^3+1320 x^4+612 x^5+150 x^6+15 x^7) \log ^4(5)+(192 x+480 x^2+480 x^3+240 x^4+60 x^5+6 x^6) \log ^5(5)+(32+80 x+80 x^2+40 x^3+10 x^4+x^5) \log ^6(5)} \, dx\)

Optimal. Leaf size=29 \[ \left (-4+\log (2)+\frac {x+\frac {4 x^2}{4+(x+\log (5))^2}}{(2+x)^2}\right )^2 \]

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Rubi [B]  time = 5.41, antiderivative size = 1749, normalized size of antiderivative = 60.31, number of steps used = 11, number of rules used = 5, integrand size = 767, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {2074, 638, 614, 618, 204}

result too large to display

Antiderivative was successfully verified.

[In]

Int[(-4096 - 9984*x - 9600*x^2 - 4544*x^3 - 864*x^4 + 432*x^5 + 568*x^6 + 300*x^7 + 78*x^8 + 8*x^9 + (1024 + 2
560*x + 2560*x^2 + 1280*x^3 + 256*x^4 - 128*x^5 - 160*x^6 - 80*x^7 - 20*x^8 - 2*x^9)*Log[2] + (-6144*x - 8832*
x^2 - 6208*x^3 - 1664*x^4 + 832*x^5 + 776*x^6 + 276*x^7 + 48*x^8 + (1536*x + 2304*x^2 + 1664*x^3 + 448*x^4 - 2
24*x^5 - 208*x^6 - 72*x^7 - 12*x^8)*Log[2])*Log[5] + (-3072 - 5440*x - 7648*x^2 - 4128*x^3 - 528*x^4 + 444*x^5
+ 402*x^6 + 120*x^7 + (768 + 1408*x + 1984*x^2 + 1120*x^3 + 144*x^4 - 120*x^5 - 108*x^6 - 30*x^7)*Log[2])*Log
[5]^2 + (-3072*x - 2880*x^2 - 1728*x^3 - 352*x^4 + 344*x^5 + 160*x^6 + (768*x + 768*x^2 + 448*x^3 + 96*x^4 - 9
6*x^5 - 40*x^6)*Log[2])*Log[5]^3 + (-768 - 848*x - 1256*x^2 - 460*x^3 + 210*x^4 + 120*x^5 + (192 + 224*x + 320
*x^2 + 128*x^3 - 60*x^4 - 30*x^5)*Log[2])*Log[5]^4 + (-384*x - 168*x^2 + 84*x^3 + 48*x^4 + (96*x + 48*x^2 - 24
*x^3 - 12*x^4)*Log[2])*Log[5]^5 + (-64 - 28*x + 14*x^2 + 8*x^3 + (16 + 8*x - 4*x^2 - 2*x^3)*Log[2])*Log[5]^6)/
(2048 + 5120*x + 6656*x^2 + 6400*x^3 + 4864*x^4 + 2944*x^5 + 1472*x^6 + 608*x^7 + 200*x^8 + 52*x^9 + 10*x^10 +
x^11 + (3072*x + 7680*x^2 + 9216*x^3 + 7680*x^4 + 4992*x^5 + 2496*x^6 + 960*x^7 + 288*x^8 + 60*x^9 + 6*x^10)*
Log[5] + (1536 + 3840*x + 6144*x^2 + 7680*x^3 + 6720*x^4 + 4128*x^5 + 1920*x^6 + 672*x^7 + 150*x^8 + 15*x^9)*L
og[5]^2 + (1536*x + 3840*x^2 + 4480*x^3 + 3520*x^4 + 2080*x^5 + 848*x^6 + 200*x^7 + 20*x^8)*Log[5]^3 + (384 +
960*x + 1440*x^2 + 1680*x^3 + 1320*x^4 + 612*x^5 + 150*x^6 + 15*x^7)*Log[5]^4 + (192*x + 480*x^2 + 480*x^3 + 2
40*x^4 + 60*x^5 + 6*x^6)*Log[5]^5 + (32 + 80*x + 80*x^2 + 40*x^3 + 10*x^4 + x^5)*Log[5]^6),x]

[Out]

(4*(4 - Log[5])^2*Log[5]^2)/((2 + x)^4*(8 - 4*Log[5] + Log[5]^2)^2) - (4*(4 - Log[5])*Log[5]^2*(32 - 16*Log[5]
+ 8*Log[5]^2 - Log[5]^3))/((2 + x)^3*(8 - 4*Log[5] + Log[5]^2)^3) - (Log[5]*(34816 - 59904*Log[5] + 50688*Log
[5]^2 - 26432*Log[5]^3 + 8960*Log[5]^4 - 2000*Log[5]^5 + 272*Log[5]^6 - 17*Log[5]^7 - 4*Log[2]*(4 - Log[5])*(8
- 4*Log[5] + Log[5]^2)^3))/((2 + x)^2*(8 - 4*Log[5] + Log[5]^2)^4) - (2*Log[5]*(Log[2]*(8 - 4*Log[5] + Log[5]
^2)^3*(32 - 16*Log[5] + 8*Log[5]^2 - Log[5]^3) - 4*(17408 - 33792*Log[5] + 35712*Log[5]^2 - 24480*Log[5]^3 + 1
1888*Log[5]^4 - 4180*Log[5]^5 + 1052*Log[5]^6 - 183*Log[5]^7 + 20*Log[5]^8 - Log[5]^9)))/((2 + x)*(8 - 4*Log[5
] + Log[5]^2)^5) - (384*ArcTan[(2*x + Log[25])/Sqrt[16 + 4*Log[5]^2 - Log[25]^2]]*(2*Log[5]*(4 + Log[5]^2)*(25
6 - 384*Log[5] + 256*Log[5]^2 - 128*Log[5]^3 + 36*Log[5]^4 - 8*Log[5]^5 + Log[5]^6) + (32 - 4*Log[5]^2 + 4*Log
[5]^3 - Log[5]^4)*(32 - 32*Log[5] + 20*Log[5]^2 - 4*Log[5]^3 + Log[5]^4)*Log[25]))/((8 - 4*Log[5] + Log[5]^2)^
4*(16 + 4*Log[5]^2 - Log[25]^2)^(5/2)) - (96*(2*x + Log[25])*(2*Log[5]*(4 + Log[5]^2)*(256 - 384*Log[5] + 256*
Log[5]^2 - 128*Log[5]^3 + 36*Log[5]^4 - 8*Log[5]^5 + Log[5]^6) + (32 - 4*Log[5]^2 + 4*Log[5]^3 - Log[5]^4)*(32
- 32*Log[5] + 20*Log[5]^2 - 4*Log[5]^3 + Log[5]^4)*Log[25]))/((8 - 4*Log[5] + Log[5]^2)^4*(4 + x^2 + Log[5]^2
+ x*Log[25])*(16 + 4*Log[5]^2 - Log[25]^2)^2) + (16*ArcTan[(2*x + Log[25])/Sqrt[16 + 4*Log[5]^2 - Log[25]^2]]
*(32768 - 64512*Log[5] + 68608*Log[5]^2 - 46208*Log[5]^3 + 21600*Log[5]^4 - 7056*Log[5]^5 + 1580*Log[5]^6 - 22
8*Log[5]^7 + 17*Log[5]^8 - 4*Log[2]*(8 - 4*Log[5] + Log[5]^2)^3*(4 - 2*Log[5] + Log[5]^2)))/((8 - 4*Log[5] + L
og[5]^2)^5*Sqrt[16 + 4*Log[5]^2 - Log[25]^2]) - (32*(x*(2*Log[5]*(4 + Log[5]^2)*(256 - 384*Log[5] + 256*Log[5]
^2 - 128*Log[5]^3 + 36*Log[5]^4 - 8*Log[5]^5 + Log[5]^6) + (32 - 4*Log[5]^2 + 4*Log[5]^3 - Log[5]^4)*(32 - 32*
Log[5] + 20*Log[5]^2 - 4*Log[5]^3 + Log[5]^4)*Log[25]) + (4 + Log[5]^2)*(2*(32 - 4*Log[5]^2 + 4*Log[5]^3 - Log
[5]^4)*(32 - 32*Log[5] + 20*Log[5]^2 - 4*Log[5]^3 + Log[5]^4) + Log[5]*(256 - 384*Log[5] + 256*Log[5]^2 - 128*
Log[5]^3 + 36*Log[5]^4 - 8*Log[5]^5 + Log[5]^6)*Log[25])))/((8 - 4*Log[5] + Log[5]^2)^4*(4 + x^2 + Log[5]^2 +
x*Log[25])^2*(16 + 4*Log[5]^2 - Log[25]^2)) - (16*((131072 - 266240*Log[5] + 322560*Log[5]^2 - 272384*Log[5]^3
+ 175872*Log[5]^4 - 89280*Log[5]^5 + 35984*Log[5]^6 - 11520*Log[5]^7 + 2848*Log[5]^8 - 516*Log[5]^9 + 63*Log[
5]^10 - 4*Log[5]^11 - Log[2]*(8 - 4*Log[5] + Log[5]^2)^3*(64 - 32*Log[5] + 32*Log[5]^2 - 12*Log[5]^3 + 4*Log[5
]^4 - Log[5]^5))*Log[25] + x*(2*(131072 - 266240*Log[5] + 322560*Log[5]^2 - 272384*Log[5]^3 + 175872*Log[5]^4
- 89280*Log[5]^5 + 35984*Log[5]^6 - 11520*Log[5]^7 + 2848*Log[5]^8 - 516*Log[5]^9 + 63*Log[5]^10 - 4*Log[5]^11
- Log[2]*(8 - 4*Log[5] + Log[5]^2)^3*(64 - 32*Log[5] + 32*Log[5]^2 - 12*Log[5]^3 + 4*Log[5]^4 - Log[5]^5)) -
Log[25]*(4096 + 256*(303 - 80*Log[2])*Log[5]^3 - 192*(293 - 76*Log[2])*Log[5]^4 + 96*(295 - 76*Log[2])*Log[5]^
5 - 32*(324 - 83*Log[2])*Log[5]^6 + 4*(689 - 176*Log[2])*Log[5]^7 + (63 - 16*Log[2])*Log[5]^9 - (4 - Log[2])*L
og[5]^10 - 6144*Log[5]^2*(11 - Log[8]) + 2048*Log[5]*(13 - Log[16]) - 12*Log[5]^8*(43 - Log[2048]))) - 2*(4 +
Log[5]^2)*(4096 + 256*(303 - 80*Log[2])*Log[5]^3 - 192*(293 - 76*Log[2])*Log[5]^4 + 96*(295 - 76*Log[2])*Log[5
]^5 - 32*(324 - 83*Log[2])*Log[5]^6 + 4*(689 - 176*Log[2])*Log[5]^7 + (63 - 16*Log[2])*Log[5]^9 - (4 - Log[2])
*Log[5]^10 - 6144*Log[5]^2*(11 - Log[8]) + 2048*Log[5]*(13 - Log[16]) - 12*Log[5]^8*(43 - Log[2048]))))/((8 -
4*Log[5] + Log[5]^2)^5*(4 + x^2 + Log[5]^2 + x*Log[25])*(16 + 4*Log[5]^2 - Log[25]^2)) - (32*ArcTan[(2*x + Log
[25])/Sqrt[16 + 4*Log[5]^2 - Log[25]^2]]*(2*(131072 - 266240*Log[5] + 322560*Log[5]^2 - 272384*Log[5]^3 + 1758
72*Log[5]^4 - 89280*Log[5]^5 + 35984*Log[5]^6 - 11520*Log[5]^7 + 2848*Log[5]^8 - 516*Log[5]^9 + 63*Log[5]^10 -
4*Log[5]^11 - Log[2]*(8 - 4*Log[5] + Log[5]^2)^3*(64 - 32*Log[5] + 32*Log[5]^2 - 12*Log[5]^3 + 4*Log[5]^4 - L
og[5]^5)) - Log[25]*(4096 + 256*(303 - 80*Log[2])*Log[5]^3 - 192*(293 - 76*Log[2])*Log[5]^4 + 96*(295 - 76*Log
[2])*Log[5]^5 - 32*(324 - 83*Log[2])*Log[5]^6 + 4*(689 - 176*Log[2])*Log[5]^7 + (63 - 16*Log[2])*Log[5]^9 - (4
- Log[2])*Log[5]^10 - 6144*Log[5]^2*(11 - Log[8]) + 2048*Log[5]*(13 - Log[16]) - 12*Log[5]^8*(43 - Log[2048])
)))/((8 - 4*Log[5] + Log[5]^2)^5*(16 + 4*Log[5]^2 - Log[25]^2)^(3/2))

Rule 204

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /
; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])

Rule 614

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((b + 2*c*x)*(a + b*x + c*x^2)^(p + 1))/((p +
1)*(b^2 - 4*a*c)), x] - Dist[(2*c*(2*p + 3))/((p + 1)*(b^2 - 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1), x], x] /;
FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1] && NeQ[p, -3/2] && IntegerQ[4*p]

Rule 618

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 638

Int[((d_.) + (e_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((b*d - 2*a*e + (2*c*d -
b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] - Dist[((2*p + 3)*(2*c*d - b*e))/((p + 1)*(b^2
- 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[2*c*d - b*e, 0] && NeQ[b^
2 - 4*a*c, 0] && LtQ[p, -1] && NeQ[p, -3/2]

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} &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 10.66, size = 33759, normalized size = 1164.10 \begin {gather*} \text {Result too large to show} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4096 - 9984*x - 9600*x^2 - 4544*x^3 - 864*x^4 + 432*x^5 + 568*x^6 + 300*x^7 + 78*x^8 + 8*x^9 + (10
24 + 2560*x + 2560*x^2 + 1280*x^3 + 256*x^4 - 128*x^5 - 160*x^6 - 80*x^7 - 20*x^8 - 2*x^9)*Log[2] + (-6144*x -
8832*x^2 - 6208*x^3 - 1664*x^4 + 832*x^5 + 776*x^6 + 276*x^7 + 48*x^8 + (1536*x + 2304*x^2 + 1664*x^3 + 448*x
^4 - 224*x^5 - 208*x^6 - 72*x^7 - 12*x^8)*Log[2])*Log[5] + (-3072 - 5440*x - 7648*x^2 - 4128*x^3 - 528*x^4 + 4
44*x^5 + 402*x^6 + 120*x^7 + (768 + 1408*x + 1984*x^2 + 1120*x^3 + 144*x^4 - 120*x^5 - 108*x^6 - 30*x^7)*Log[2
])*Log[5]^2 + (-3072*x - 2880*x^2 - 1728*x^3 - 352*x^4 + 344*x^5 + 160*x^6 + (768*x + 768*x^2 + 448*x^3 + 96*x
^4 - 96*x^5 - 40*x^6)*Log[2])*Log[5]^3 + (-768 - 848*x - 1256*x^2 - 460*x^3 + 210*x^4 + 120*x^5 + (192 + 224*x
+ 320*x^2 + 128*x^3 - 60*x^4 - 30*x^5)*Log[2])*Log[5]^4 + (-384*x - 168*x^2 + 84*x^3 + 48*x^4 + (96*x + 48*x^
2 - 24*x^3 - 12*x^4)*Log[2])*Log[5]^5 + (-64 - 28*x + 14*x^2 + 8*x^3 + (16 + 8*x - 4*x^2 - 2*x^3)*Log[2])*Log[
5]^6)/(2048 + 5120*x + 6656*x^2 + 6400*x^3 + 4864*x^4 + 2944*x^5 + 1472*x^6 + 608*x^7 + 200*x^8 + 52*x^9 + 10*
x^10 + x^11 + (3072*x + 7680*x^2 + 9216*x^3 + 7680*x^4 + 4992*x^5 + 2496*x^6 + 960*x^7 + 288*x^8 + 60*x^9 + 6*
x^10)*Log[5] + (1536 + 3840*x + 6144*x^2 + 7680*x^3 + 6720*x^4 + 4128*x^5 + 1920*x^6 + 672*x^7 + 150*x^8 + 15*
x^9)*Log[5]^2 + (1536*x + 3840*x^2 + 4480*x^3 + 3520*x^4 + 2080*x^5 + 848*x^6 + 200*x^7 + 20*x^8)*Log[5]^3 + (
384 + 960*x + 1440*x^2 + 1680*x^3 + 1320*x^4 + 612*x^5 + 150*x^6 + 15*x^7)*Log[5]^4 + (192*x + 480*x^2 + 480*x
^3 + 240*x^4 + 60*x^5 + 6*x^6)*Log[5]^5 + (32 + 80*x + 80*x^2 + 40*x^3 + 10*x^4 + x^5)*Log[5]^6),x]

[Out]

Result too large to show

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fricas [B]  time = 0.57, size = 426, normalized size = 14.69 \begin {gather*} -\frac {8 \, x^{7} + 63 \, x^{6} + 216 \, x^{5} + {\left (8 \, x^{3} + 31 \, x^{2} - 2 \, {\left (x^{3} + 4 \, x^{2} + 4 \, x\right )} \log \relax (2) + 32 \, x\right )} \log \relax (5)^{4} + 488 \, x^{4} + 4 \, {\left (8 \, x^{4} + 31 \, x^{3} + 32 \, x^{2} - 2 \, {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} \log \relax (2)\right )} \log \relax (5)^{3} + 864 \, x^{3} + 2 \, {\left (24 \, x^{5} + 109 \, x^{4} + 188 \, x^{3} + 188 \, x^{2} - 2 \, {\left (3 \, x^{5} + 14 \, x^{4} + 24 \, x^{3} + 24 \, x^{2} + 16 \, x\right )} \log \relax (2) + 128 \, x\right )} \log \relax (5)^{2} + 1008 \, x^{2} + 4 \, {\left (8 \, x^{6} + 47 \, x^{5} + 124 \, x^{4} + 188 \, x^{3} + 128 \, x^{2} - 2 \, {\left (x^{6} + 6 \, x^{5} + 16 \, x^{4} + 24 \, x^{3} + 16 \, x^{2}\right )} \log \relax (2)\right )} \log \relax (5) - 2 \, {\left (x^{7} + 8 \, x^{6} + 28 \, x^{5} + 64 \, x^{4} + 112 \, x^{3} + 128 \, x^{2} + 64 \, x\right )} \log \relax (2) + 512 \, x}{x^{8} + 8 \, x^{7} + 32 \, x^{6} + 96 \, x^{5} + {\left (x^{4} + 8 \, x^{3} + 24 \, x^{2} + 32 \, x + 16\right )} \log \relax (5)^{4} + 224 \, x^{4} + 4 \, {\left (x^{5} + 8 \, x^{4} + 24 \, x^{3} + 32 \, x^{2} + 16 \, x\right )} \log \relax (5)^{3} + 384 \, x^{3} + 2 \, {\left (3 \, x^{6} + 24 \, x^{5} + 76 \, x^{4} + 128 \, x^{3} + 144 \, x^{2} + 128 \, x + 64\right )} \log \relax (5)^{2} + 512 \, x^{2} + 4 \, {\left (x^{7} + 8 \, x^{6} + 28 \, x^{5} + 64 \, x^{4} + 112 \, x^{3} + 128 \, x^{2} + 64 \, x\right )} \log \relax (5) + 512 \, x + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^3-4*x^2+8*x+16)*log(2)+8*x^3+14*x^2-28*x-64)*log(5)^6+((-12*x^4-24*x^3+48*x^2+96*x)*log(2)+4
8*x^4+84*x^3-168*x^2-384*x)*log(5)^5+((-30*x^5-60*x^4+128*x^3+320*x^2+224*x+192)*log(2)+120*x^5+210*x^4-460*x^
3-1256*x^2-848*x-768)*log(5)^4+((-40*x^6-96*x^5+96*x^4+448*x^3+768*x^2+768*x)*log(2)+160*x^6+344*x^5-352*x^4-1
728*x^3-2880*x^2-3072*x)*log(5)^3+((-30*x^7-108*x^6-120*x^5+144*x^4+1120*x^3+1984*x^2+1408*x+768)*log(2)+120*x
^7+402*x^6+444*x^5-528*x^4-4128*x^3-7648*x^2-5440*x-3072)*log(5)^2+((-12*x^8-72*x^7-208*x^6-224*x^5+448*x^4+16
64*x^3+2304*x^2+1536*x)*log(2)+48*x^8+276*x^7+776*x^6+832*x^5-1664*x^4-6208*x^3-8832*x^2-6144*x)*log(5)+(-2*x^
9-20*x^8-80*x^7-160*x^6-128*x^5+256*x^4+1280*x^3+2560*x^2+2560*x+1024)*log(2)+8*x^9+78*x^8+300*x^7+568*x^6+432
*x^5-864*x^4-4544*x^3-9600*x^2-9984*x-4096)/((x^5+10*x^4+40*x^3+80*x^2+80*x+32)*log(5)^6+(6*x^6+60*x^5+240*x^4
+480*x^3+480*x^2+192*x)*log(5)^5+(15*x^7+150*x^6+612*x^5+1320*x^4+1680*x^3+1440*x^2+960*x+384)*log(5)^4+(20*x^
8+200*x^7+848*x^6+2080*x^5+3520*x^4+4480*x^3+3840*x^2+1536*x)*log(5)^3+(15*x^9+150*x^8+672*x^7+1920*x^6+4128*x
^5+6720*x^4+7680*x^3+6144*x^2+3840*x+1536)*log(5)^2+(6*x^10+60*x^9+288*x^8+960*x^7+2496*x^6+4992*x^5+7680*x^4+
9216*x^3+7680*x^2+3072*x)*log(5)+x^11+10*x^10+52*x^9+200*x^8+608*x^7+1472*x^6+2944*x^5+4864*x^4+6400*x^3+6656*
x^2+5120*x+2048),x, algorithm="fricas")

[Out]

-(8*x^7 + 63*x^6 + 216*x^5 + (8*x^3 + 31*x^2 - 2*(x^3 + 4*x^2 + 4*x)*log(2) + 32*x)*log(5)^4 + 488*x^4 + 4*(8*
x^4 + 31*x^3 + 32*x^2 - 2*(x^4 + 4*x^3 + 4*x^2)*log(2))*log(5)^3 + 864*x^3 + 2*(24*x^5 + 109*x^4 + 188*x^3 + 1
88*x^2 - 2*(3*x^5 + 14*x^4 + 24*x^3 + 24*x^2 + 16*x)*log(2) + 128*x)*log(5)^2 + 1008*x^2 + 4*(8*x^6 + 47*x^5 +
124*x^4 + 188*x^3 + 128*x^2 - 2*(x^6 + 6*x^5 + 16*x^4 + 24*x^3 + 16*x^2)*log(2))*log(5) - 2*(x^7 + 8*x^6 + 28
*x^5 + 64*x^4 + 112*x^3 + 128*x^2 + 64*x)*log(2) + 512*x)/(x^8 + 8*x^7 + 32*x^6 + 96*x^5 + (x^4 + 8*x^3 + 24*x
^2 + 32*x + 16)*log(5)^4 + 224*x^4 + 4*(x^5 + 8*x^4 + 24*x^3 + 32*x^2 + 16*x)*log(5)^3 + 384*x^3 + 2*(3*x^6 +
24*x^5 + 76*x^4 + 128*x^3 + 144*x^2 + 128*x + 64)*log(5)^2 + 512*x^2 + 4*(x^7 + 8*x^6 + 28*x^5 + 64*x^4 + 112*
x^3 + 128*x^2 + 64*x)*log(5) + 512*x + 256)

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giac [B]  time = 1.22, size = 1494, normalized size = 51.52 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^3-4*x^2+8*x+16)*log(2)+8*x^3+14*x^2-28*x-64)*log(5)^6+((-12*x^4-24*x^3+48*x^2+96*x)*log(2)+4
8*x^4+84*x^3-168*x^2-384*x)*log(5)^5+((-30*x^5-60*x^4+128*x^3+320*x^2+224*x+192)*log(2)+120*x^5+210*x^4-460*x^
3-1256*x^2-848*x-768)*log(5)^4+((-40*x^6-96*x^5+96*x^4+448*x^3+768*x^2+768*x)*log(2)+160*x^6+344*x^5-352*x^4-1
728*x^3-2880*x^2-3072*x)*log(5)^3+((-30*x^7-108*x^6-120*x^5+144*x^4+1120*x^3+1984*x^2+1408*x+768)*log(2)+120*x
^7+402*x^6+444*x^5-528*x^4-4128*x^3-7648*x^2-5440*x-3072)*log(5)^2+((-12*x^8-72*x^7-208*x^6-224*x^5+448*x^4+16
64*x^3+2304*x^2+1536*x)*log(2)+48*x^8+276*x^7+776*x^6+832*x^5-1664*x^4-6208*x^3-8832*x^2-6144*x)*log(5)+(-2*x^
9-20*x^8-80*x^7-160*x^6-128*x^5+256*x^4+1280*x^3+2560*x^2+2560*x+1024)*log(2)+8*x^9+78*x^8+300*x^7+568*x^6+432
*x^5-864*x^4-4544*x^3-9600*x^2-9984*x-4096)/((x^5+10*x^4+40*x^3+80*x^2+80*x+32)*log(5)^6+(6*x^6+60*x^5+240*x^4
+480*x^3+480*x^2+192*x)*log(5)^5+(15*x^7+150*x^6+612*x^5+1320*x^4+1680*x^3+1440*x^2+960*x+384)*log(5)^4+(20*x^
8+200*x^7+848*x^6+2080*x^5+3520*x^4+4480*x^3+3840*x^2+1536*x)*log(5)^3+(15*x^9+150*x^8+672*x^7+1920*x^6+4128*x
^5+6720*x^4+7680*x^3+6144*x^2+3840*x+1536)*log(5)^2+(6*x^10+60*x^9+288*x^8+960*x^7+2496*x^6+4992*x^5+7680*x^4+
9216*x^3+7680*x^2+3072*x)*log(5)+x^11+10*x^10+52*x^9+200*x^8+608*x^7+1472*x^6+2944*x^5+4864*x^4+6400*x^3+6656*
x^2+5120*x+2048),x, algorithm="giac")

[Out]

8*(x^2*log(5)^10*log(2) + 2*x*log(5)^11*log(2) + log(5)^12*log(2) - 4*x^2*log(5)^10 - 8*x*log(5)^11 - 4*log(5)
^12 + 4*x^3*log(5)^8*log(2) - 4*x^2*log(5)^9*log(2) - 20*x*log(5)^10*log(2) - 12*log(5)^11*log(2) - 17*x^3*log
(5)^8 + 12*x^2*log(5)^9 + 75*x*log(5)^10 + 46*log(5)^11 - 56*x^3*log(5)^7*log(2) - 36*x^2*log(5)^8*log(2) + 96
*x*log(5)^9*log(2) + 80*log(5)^10*log(2) + 228*x^3*log(5)^7 + 168*x^2*log(5)^8 - 348*x*log(5)^9 - 302*log(5)^1
0 + 400*x^3*log(5)^6*log(2) + 496*x^2*log(5)^7*log(2) - 192*x*log(5)^8*log(2) - 352*log(5)^9*log(2) - 1580*x^3
*log(5)^6 - 1984*x^2*log(5)^7 + 720*x*log(5)^8 + 1352*log(5)^9 - 1792*x^3*log(5)^5*log(2) - 2720*x^2*log(5)^6*
log(2) - 288*x*log(5)^7*log(2) + 1168*log(5)^8*log(2) + 7056*x^3*log(5)^5 + 10800*x^2*log(5)^6 + 1184*x*log(5)
^7 - 4464*log(5)^8 + 5504*x^3*log(5)^4*log(2) + 9216*x^2*log(5)^5*log(2) + 3520*x*log(5)^6*log(2) - 3008*log(5
)^7*log(2) - 21600*x^3*log(5)^4 - 36480*x^2*log(5)^5 - 13584*x*log(5)^6 + 11616*log(5)^7 - 11776*x^3*log(5)^3*
log(2) - 20736*x^2*log(5)^4*log(2) - 13312*x*log(5)^5*log(2) + 6272*log(5)^6*log(2) + 46208*x^3*log(5)^3 + 823
68*x^2*log(5)^4 + 51136*x*log(5)^5 - 24416*log(5)^6 + 17408*x^3*log(5)^2*log(2) + 31744*x^2*log(5)^3*log(2) +
33280*x*log(5)^4*log(2) - 10240*log(5)^5*log(2) - 68608*x^3*log(5)^2 - 128256*x^2*log(5)^3 - 129152*x*log(5)^4
+ 39808*log(5)^5 - 16384*x^3*log(5)*log(2) - 30720*x^2*log(5)^2*log(2) - 59392*x*log(5)^3*log(2) + 13312*log(
5)^4*log(2) + 64512*x^3*log(5) + 125952*x^2*log(5)^2 + 229888*x*log(5)^3 - 53248*log(5)^4 + 8192*x^3*log(2) +
16384*x^2*log(5)*log(2) + 77824*x*log(5)^2*log(2) - 12288*log(5)^3*log(2) - 32768*x^3 - 71680*x^2*log(5) - 305
152*x*log(5)^2 + 48128*log(5)^3 - 65536*x*log(5)*log(2) + 8192*log(5)^2*log(2) + 4096*x^2 + 258048*x*log(5) -
34816*log(5)^2 + 32768*x*log(2) - 131072*x)/((log(5)^10 - 20*log(5)^9 + 200*log(5)^8 - 1280*log(5)^7 + 5760*lo
g(5)^6 - 18944*log(5)^5 + 46080*log(5)^4 - 81920*log(5)^3 + 102400*log(5)^2 - 81920*log(5) + 32768)*(x^2 + 2*x
*log(5) + log(5)^2 + 4)^2) + (2*x^3*log(5)^10*log(2) - 8*x^3*log(5)^10 - 40*x^3*log(5)^9*log(2) + 8*x^2*log(5)
^10*log(2) + 160*x^3*log(5)^9 - 31*x^2*log(5)^10 + 368*x^3*log(5)^8*log(2) - 160*x^2*log(5)^9*log(2) + 8*x*log
(5)^10*log(2) - 1464*x^3*log(5)^8 + 620*x^2*log(5)^9 - 32*x*log(5)^10 - 2112*x^3*log(5)^7*log(2) + 1440*x^2*lo
g(5)^8*log(2) - 160*x*log(5)^9*log(2) + 8416*x^3*log(5)^7 - 5560*x^2*log(5)^8 + 640*x*log(5)^9 + 8320*x^3*log(
5)^6*log(2) - 8064*x^2*log(5)^7*log(2) + 1344*x*log(5)^8*log(2) - 33440*x^3*log(5)^6 + 31360*x^2*log(5)^7 - 53
76*x*log(5)^8 - 23552*x^3*log(5)^5*log(2) + 30976*x^2*log(5)^6*log(2) - 6912*x*log(5)^7*log(2) - 128*log(5)^8*
log(2) + 95104*x^3*log(5)^5 - 122368*x^2*log(5)^6 + 28160*x*log(5)^7 + 512*log(5)^8 + 48128*x^3*log(5)^4*log(2
) - 86016*x^2*log(5)^5*log(2) + 24064*x*log(5)^6*log(2) + 1536*log(5)^7*log(2) - 195840*x^3*log(5)^4 + 342528*
x^2*log(5)^5 - 101248*x*log(5)^6 - 5888*log(5)^7 - 69632*x^3*log(5)^3*log(2) + 174080*x^2*log(5)^4*log(2) - 61
440*x*log(5)^5*log(2) - 9216*log(5)^6*log(2) + 285696*x^3*log(5)^3 - 700928*x^2*log(5)^4 + 260608*x*log(5)^5 +
34560*log(5)^6 + 65536*x^3*log(5)^2*log(2) - 253952*x^2*log(5)^3*log(2) + 118784*x*log(5)^4*log(2) + 32768*lo
g(5)^5*log(2) - 270336*x^3*log(5)^2 + 1034240*x^2*log(5)^3 - 506880*x*log(5)^4 - 125952*log(5)^5 - 32768*x^3*l
og(5)*log(2) + 245760*x^2*log(5)^2*log(2) - 180224*x*log(5)^3*log(2) - 73728*log(5)^4*log(2) + 139264*x^3*log(
5) - 1003520*x^2*log(5)^2 + 765952*x*log(5)^3 + 286720*log(5)^4 - 131072*x^2*log(5)*log(2) + 196608*x*log(5)^2
*log(2) + 98304*log(5)^3*log(2) + 557056*x^2*log(5) - 802816*x*log(5)^2 - 385024*log(5)^3 - 131072*x*log(5)*lo
g(2) - 65536*log(5)^2*log(2) + 557056*x*log(5) + 278528*log(5)^2)/((log(5)^10 - 20*log(5)^9 + 200*log(5)^8 - 1
280*log(5)^7 + 5760*log(5)^6 - 18944*log(5)^5 + 46080*log(5)^4 - 81920*log(5)^3 + 102400*log(5)^2 - 81920*log(
5) + 32768)*(x + 2)^4)

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maple [B]  time = 0.83, size = 296, normalized size = 10.21

method	result	size
norman	\(\frac {\left (2 \ln \relax (2)-8\right ) x^{7}+\left (8 \ln \relax (2) \ln \relax (5)+16 \ln \relax (2)-32 \ln \relax (5)-63\right ) x^{6}+\left (12 \ln \relax (2) \ln \relax (5)^{2}+48 \ln \relax (2) \ln \relax (5)-48 \ln \relax (5)^{2}+56 \ln \relax (2)-188 \ln \relax (5)-216\right ) x^{5}+\left (8 \ln \relax (2) \ln \relax (5)^{4}-32 \ln \relax (5)^{4}+64 \ln \relax (2) \ln \relax (5)^{2}-256 \ln \relax (5)^{2}+128 \ln \relax (2)-512\right ) x +\left (8 \ln \relax (2) \ln \relax (5)^{3}+56 \ln \relax (2) \ln \relax (5)^{2}-32 \ln \relax (5)^{3}+128 \ln \relax (2) \ln \relax (5)-218 \ln \relax (5)^{2}+128 \ln \relax (2)-496 \ln \relax (5)-488\right ) x^{4}+\left (2 \ln \relax (2) \ln \relax (5)^{4}+32 \ln \relax (2) \ln \relax (5)^{3}-8 \ln \relax (5)^{4}+96 \ln \relax (2) \ln \relax (5)^{2}-124 \ln \relax (5)^{3}+192 \ln \relax (2) \ln \relax (5)-376 \ln \relax (5)^{2}+224 \ln \relax (2)-752 \ln \relax (5)-864\right ) x^{3}+\left (8 \ln \relax (2) \ln \relax (5)^{4}+32 \ln \relax (2) \ln \relax (5)^{3}-31 \ln \relax (5)^{4}+96 \ln \relax (2) \ln \relax (5)^{2}-128 \ln \relax (5)^{3}+128 \ln \relax (2) \ln \relax (5)-376 \ln \relax (5)^{2}+256 \ln \relax (2)-512 \ln \relax (5)-1008\right ) x^{2}}{\left (2+x \right )^{4} \left (\ln \relax (5)^{2}+2 x \ln \relax (5)+x^{2}+4\right )^{2}}\)	\(296\)
risch	\(\frac {\left (2 \ln \relax (2)-8\right ) x^{7}+\left (8 \ln \relax (2) \ln \relax (5)+16 \ln \relax (2)-32 \ln \relax (5)-63\right ) x^{6}+\left (12 \ln \relax (2) \ln \relax (5)^{2}+48 \ln \relax (2) \ln \relax (5)-48 \ln \relax (5)^{2}+56 \ln \relax (2)-188 \ln \relax (5)-216\right ) x^{5}+\left (8 \ln \relax (2) \ln \relax (5)^{4}-32 \ln \relax (5)^{4}+64 \ln \relax (2) \ln \relax (5)^{2}-256 \ln \relax (5)^{2}+128 \ln \relax (2)-512\right ) x +\left (8 \ln \relax (2) \ln \relax (5)^{3}+56 \ln \relax (2) \ln \relax (5)^{2}-32 \ln \relax (5)^{3}+128 \ln \relax (2) \ln \relax (5)-218 \ln \relax (5)^{2}+128 \ln \relax (2)-496 \ln \relax (5)-488\right ) x^{4}+\left (2 \ln \relax (2) \ln \relax (5)^{4}+32 \ln \relax (2) \ln \relax (5)^{3}-8 \ln \relax (5)^{4}+96 \ln \relax (2) \ln \relax (5)^{2}-124 \ln \relax (5)^{3}+192 \ln \relax (2) \ln \relax (5)-376 \ln \relax (5)^{2}+224 \ln \relax (2)-752 \ln \relax (5)-864\right ) x^{3}+\left (8 \ln \relax (2) \ln \relax (5)^{4}+32 \ln \relax (2) \ln \relax (5)^{3}-31 \ln \relax (5)^{4}+96 \ln \relax (2) \ln \relax (5)^{2}-128 \ln \relax (5)^{3}+128 \ln \relax (2) \ln \relax (5)-376 \ln \relax (5)^{2}+256 \ln \relax (2)-512 \ln \relax (5)-1008\right ) x^{2}}{256+512 x +256 x^{3} \ln \relax (5)^{2}+48 x^{5} \ln \relax (5)^{2}+x^{4} \ln \relax (5)^{4}+6 x^{6} \ln \relax (5)^{2}+512 x^{2} \ln \relax (5)+16 \ln \relax (5)^{4}+32 x^{4} \ln \relax (5)^{3}+4 x^{5} \ln \relax (5)^{3}+128 \ln \relax (5)^{2}+8 x^{7}+x^{8}+224 x^{4}+384 x^{3}+512 x^{2}+32 x^{6}+96 x^{5}+96 x^{3} \ln \relax (5)^{3}+112 x^{5} \ln \relax (5)+32 x^{6} \ln \relax (5)+32 x \ln \relax (5)^{4}+256 x \ln \relax (5)+288 x^{2} \ln \relax (5)^{2}+448 x^{3} \ln \relax (5)+8 x^{3} \ln \relax (5)^{4}+4 x^{7} \ln \relax (5)+64 \ln \relax (5)^{3} x +24 \ln \relax (5)^{4} x^{2}+152 x^{4} \ln \relax (5)^{2}+256 x \ln \relax (5)^{2}+256 x^{4} \ln \relax (5)+128 x^{2} \ln \relax (5)^{3}}\)	\(502\)
gosper	\(\frac {x \left (-512+192 x^{2} \ln \relax (2) \ln \relax (5)-1008 x -218 x^{3} \ln \relax (5)^{2}+48 x^{4} \ln \relax (5) \ln \relax (2)+96 x \ln \relax (2) \ln \relax (5)^{2}+128 x \ln \relax (2) \ln \relax (5)-752 x^{2} \ln \relax (5)-32 \ln \relax (5)^{4}-256 \ln \relax (5)^{2}+128 \ln \relax (2)-216 x^{4}-488 x^{3}-864 x^{2}-8 x^{6}-63 x^{5}-32 x^{3} \ln \relax (5)^{3}-32 x^{5} \ln \relax (5)-31 x \ln \relax (5)^{4}+56 x^{4} \ln \relax (2)+16 x^{5} \ln \relax (2)+2 x^{6} \ln \relax (2)-512 x \ln \relax (5)-376 x^{2} \ln \relax (5)^{2}-496 x^{3} \ln \relax (5)+256 x \ln \relax (2)+224 x^{2} \ln \relax (2)+128 x^{3} \ln \relax (2)+8 \ln \relax (2) \ln \relax (5)^{4}-128 \ln \relax (5)^{3} x +64 \ln \relax (2) \ln \relax (5)^{2}-8 \ln \relax (5)^{4} x^{2}-48 x^{4} \ln \relax (5)^{2}-376 x \ln \relax (5)^{2}-188 x^{4} \ln \relax (5)-124 x^{2} \ln \relax (5)^{3}+2 \ln \relax (2) \ln \relax (5)^{4} x^{2}+8 \ln \relax (2) \ln \relax (5)^{3} x^{3}+12 \ln \relax (2) \ln \relax (5)^{2} x^{4}+8 \ln \relax (2) \ln \relax (5) x^{5}+8 \ln \relax (2) \ln \relax (5)^{4} x +32 \ln \relax (2) \ln \relax (5)^{3} x^{2}+56 \ln \relax (2) \ln \relax (5)^{2} x^{3}+32 \ln \relax (2) \ln \relax (5)^{3} x +96 \ln \relax (2) \ln \relax (5)^{2} x^{2}+128 \ln \relax (2) \ln \relax (5) x^{3}\right )}{256+512 x +256 x^{3} \ln \relax (5)^{2}+48 x^{5} \ln \relax (5)^{2}+x^{4} \ln \relax (5)^{4}+6 x^{6} \ln \relax (5)^{2}+512 x^{2} \ln \relax (5)+16 \ln \relax (5)^{4}+32 x^{4} \ln \relax (5)^{3}+4 x^{5} \ln \relax (5)^{3}+128 \ln \relax (5)^{2}+8 x^{7}+x^{8}+224 x^{4}+384 x^{3}+512 x^{2}+32 x^{6}+96 x^{5}+96 x^{3} \ln \relax (5)^{3}+112 x^{5} \ln \relax (5)+32 x^{6} \ln \relax (5)+32 x \ln \relax (5)^{4}+256 x \ln \relax (5)+288 x^{2} \ln \relax (5)^{2}+448 x^{3} \ln \relax (5)+8 x^{3} \ln \relax (5)^{4}+4 x^{7} \ln \relax (5)+64 \ln \relax (5)^{3} x +24 \ln \relax (5)^{4} x^{2}+152 x^{4} \ln \relax (5)^{2}+256 x \ln \relax (5)^{2}+256 x^{4} \ln \relax (5)+128 x^{2} \ln \relax (5)^{3}}\)	\(576\)
default	\(-\frac {8 \left (4464 \ln \relax (5)^{8}-11616 \ln \relax (5)^{7}+24416 \ln \relax (5)^{6}-39808 \ln \relax (5)^{5}-48128 \ln \relax (5)^{3}+53248 \ln \relax (5)^{4}+34816 \ln \relax (5)^{2}+\left (-4 \ln \relax (2) \ln \relax (5)^{8}+56 \ln \relax (2) \ln \relax (5)^{7}+17 \ln \relax (5)^{8}-400 \ln \relax (2) \ln \relax (5)^{6}-228 \ln \relax (5)^{7}+1792 \ln \relax (2) \ln \relax (5)^{5}+1580 \ln \relax (5)^{6}-5504 \ln \relax (2) \ln \relax (5)^{4}-7056 \ln \relax (5)^{5}+11776 \ln \relax (2) \ln \relax (5)^{3}+21600 \ln \relax (5)^{4}-17408 \ln \relax (2) \ln \relax (5)^{2}-46208 \ln \relax (5)^{3}+16384 \ln \relax (2) \ln \relax (5)+68608 \ln \relax (5)^{2}-8192 \ln \relax (2)-64512 \ln \relax (5)+32768\right ) x^{3}+\left (-\ln \relax (2) \ln \relax (5)^{10}+4 \ln \relax (2) \ln \relax (5)^{9}+4 \ln \relax (5)^{10}+36 \ln \relax (2) \ln \relax (5)^{8}-12 \ln \relax (5)^{9}-496 \ln \relax (2) \ln \relax (5)^{7}-168 \ln \relax (5)^{8}+2720 \ln \relax (2) \ln \relax (5)^{6}+1984 \ln \relax (5)^{7}-9216 \ln \relax (2) \ln \relax (5)^{5}-10800 \ln \relax (5)^{6}+20736 \ln \relax (2) \ln \relax (5)^{4}+36480 \ln \relax (5)^{5}-31744 \ln \relax (2) \ln \relax (5)^{3}-82368 \ln \relax (5)^{4}+30720 \ln \relax (2) \ln \relax (5)^{2}+128256 \ln \relax (5)^{3}-16384 \ln \relax (2) \ln \relax (5)-125952 \ln \relax (5)^{2}+71680 \ln \relax (5)-4096\right ) x^{2}+\left (-2 \ln \relax (2) \ln \relax (5)^{11}+20 \ln \relax (2) \ln \relax (5)^{10}+8 \ln \relax (5)^{11}-96 \ln \relax (2) \ln \relax (5)^{9}-75 \ln \relax (5)^{10}+192 \ln \relax (2) \ln \relax (5)^{8}+348 \ln \relax (5)^{9}+288 \ln \relax (2) \ln \relax (5)^{7}-720 \ln \relax (5)^{8}-3520 \ln \relax (2) \ln \relax (5)^{6}-1184 \ln \relax (5)^{7}+13312 \ln \relax (2) \ln \relax (5)^{5}+13584 \ln \relax (5)^{6}-33280 \ln \relax (2) \ln \relax (5)^{4}-51136 \ln \relax (5)^{5}+59392 \ln \relax (2) \ln \relax (5)^{3}+129152 \ln \relax (5)^{4}-77824 \ln \relax (2) \ln \relax (5)^{2}-229888 \ln \relax (5)^{3}+65536 \ln \relax (2) \ln \relax (5)+305152 \ln \relax (5)^{2}-32768 \ln \relax (2)-258048 \ln \relax (5)+131072\right ) x -80 \ln \relax (2) \ln \relax (5)^{10}-\ln \relax (2) \ln \relax (5)^{12}+12 \ln \relax (2) \ln \relax (5)^{11}+352 \ln \relax (2) \ln \relax (5)^{9}+12288 \ln \relax (2) \ln \relax (5)^{3}+3008 \ln \relax (2) \ln \relax (5)^{7}+10240 \ln \relax (2) \ln \relax (5)^{5}-13312 \ln \relax (2) \ln \relax (5)^{4}-8192 \ln \relax (2) \ln \relax (5)^{2}-6272 \ln \relax (2) \ln \relax (5)^{6}-1168 \ln \relax (2) \ln \relax (5)^{8}+302 \ln \relax (5)^{10}-1352 \ln \relax (5)^{9}+4 \ln \relax (5)^{12}-46 \ln \relax (5)^{11}\right )}{\left (\ln \relax (5)^{2}-4 \ln \relax (5)+8\right )^{5} \left (\ln \relax (5)^{2}+2 x \ln \relax (5)+x^{2}+4\right )^{2}}-\frac {\ln \relax (5) \left (4 \ln \relax (2) \ln \relax (5)^{7}-64 \ln \relax (2) \ln \relax (5)^{6}-17 \ln \relax (5)^{7}+480 \ln \relax (2) \ln \relax (5)^{5}+272 \ln \relax (5)^{6}-2176 \ln \relax (2) \ln \relax (5)^{4}-2000 \ln \relax (5)^{5}+6400 \ln \relax (2) \ln \relax (5)^{3}+8960 \ln \relax (5)^{4}-12288 \ln \relax (2) \ln \relax (5)^{2}-26432 \ln \relax (5)^{3}+14336 \ln \relax (2) \ln \relax (5)+50688 \ln \relax (5)^{2}-8192 \ln \relax (2)-59904 \ln \relax (5)+34816\right )}{\left (\ln \relax (5)^{2}-4 \ln \relax (5)+8\right )^{4} \left (2+x \right )^{2}}+\frac {2 \ln \relax (5) \left (\ln \relax (2) \ln \relax (5)^{9}-20 \ln \relax (2) \ln \relax (5)^{8}-4 \ln \relax (5)^{9}+184 \ln \relax (2) \ln \relax (5)^{7}+80 \ln \relax (5)^{8}-1056 \ln \relax (2) \ln \relax (5)^{6}-732 \ln \relax (5)^{7}+4160 \ln \relax (2) \ln \relax (5)^{5}+4208 \ln \relax (5)^{6}-11776 \ln \relax (2) \ln \relax (5)^{4}-16720 \ln \relax (5)^{5}+24064 \ln \relax (2) \ln \relax (5)^{3}+47552 \ln \relax (5)^{4}-34816 \ln \relax (2) \ln \relax (5)^{2}-97920 \ln \relax (5)^{3}+32768 \ln \relax (2) \ln \relax (5)+142848 \ln \relax (5)^{2}-16384 \ln \relax (2)-135168 \ln \relax (5)+69632\right )}{\left (\ln \relax (5)^{2}-4 \ln \relax (5)+8\right )^{5} \left (2+x \right )}+\frac {4 \ln \relax (5)^{2} \left (\ln \relax (5)^{2}-8 \ln \relax (5)+16\right )}{\left (\ln \relax (5)^{2}-4 \ln \relax (5)+8\right )^{2} \left (2+x \right )^{4}}-\frac {4 \ln \relax (5)^{2} \left (\ln \relax (5)^{4}-12 \ln \relax (5)^{3}+48 \ln \relax (5)^{2}-96 \ln \relax (5)+128\right )}{\left (\ln \relax (5)^{2}-4 \ln \relax (5)+8\right )^{3} \left (2+x \right )^{3}}\)	\(952\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*x^3-4*x^2+8*x+16)*ln(2)+8*x^3+14*x^2-28*x-64)*ln(5)^6+((-12*x^4-24*x^3+48*x^2+96*x)*ln(2)+48*x^4+84*
x^3-168*x^2-384*x)*ln(5)^5+((-30*x^5-60*x^4+128*x^3+320*x^2+224*x+192)*ln(2)+120*x^5+210*x^4-460*x^3-1256*x^2-
848*x-768)*ln(5)^4+((-40*x^6-96*x^5+96*x^4+448*x^3+768*x^2+768*x)*ln(2)+160*x^6+344*x^5-352*x^4-1728*x^3-2880*
x^2-3072*x)*ln(5)^3+((-30*x^7-108*x^6-120*x^5+144*x^4+1120*x^3+1984*x^2+1408*x+768)*ln(2)+120*x^7+402*x^6+444*
x^5-528*x^4-4128*x^3-7648*x^2-5440*x-3072)*ln(5)^2+((-12*x^8-72*x^7-208*x^6-224*x^5+448*x^4+1664*x^3+2304*x^2+
1536*x)*ln(2)+48*x^8+276*x^7+776*x^6+832*x^5-1664*x^4-6208*x^3-8832*x^2-6144*x)*ln(5)+(-2*x^9-20*x^8-80*x^7-16
0*x^6-128*x^5+256*x^4+1280*x^3+2560*x^2+2560*x+1024)*ln(2)+8*x^9+78*x^8+300*x^7+568*x^6+432*x^5-864*x^4-4544*x
^3-9600*x^2-9984*x-4096)/((x^5+10*x^4+40*x^3+80*x^2+80*x+32)*ln(5)^6+(6*x^6+60*x^5+240*x^4+480*x^3+480*x^2+192
*x)*ln(5)^5+(15*x^7+150*x^6+612*x^5+1320*x^4+1680*x^3+1440*x^2+960*x+384)*ln(5)^4+(20*x^8+200*x^7+848*x^6+2080
*x^5+3520*x^4+4480*x^3+3840*x^2+1536*x)*ln(5)^3+(15*x^9+150*x^8+672*x^7+1920*x^6+4128*x^5+6720*x^4+7680*x^3+61
44*x^2+3840*x+1536)*ln(5)^2+(6*x^10+60*x^9+288*x^8+960*x^7+2496*x^6+4992*x^5+7680*x^4+9216*x^3+7680*x^2+3072*x
)*ln(5)+x^11+10*x^10+52*x^9+200*x^8+608*x^7+1472*x^6+2944*x^5+4864*x^4+6400*x^3+6656*x^2+5120*x+2048),x,method
=_RETURNVERBOSE)

[Out]

((2*ln(2)-8)*x^7+(8*ln(2)*ln(5)+16*ln(2)-32*ln(5)-63)*x^6+(12*ln(2)*ln(5)^2+48*ln(2)*ln(5)-48*ln(5)^2+56*ln(2)
-188*ln(5)-216)*x^5+(8*ln(2)*ln(5)^4-32*ln(5)^4+64*ln(2)*ln(5)^2-256*ln(5)^2+128*ln(2)-512)*x+(8*ln(2)*ln(5)^3
+56*ln(2)*ln(5)^2-32*ln(5)^3+128*ln(2)*ln(5)-218*ln(5)^2+128*ln(2)-496*ln(5)-488)*x^4+(2*ln(2)*ln(5)^4+32*ln(2
)*ln(5)^3-8*ln(5)^4+96*ln(2)*ln(5)^2-124*ln(5)^3+192*ln(2)*ln(5)-376*ln(5)^2+224*ln(2)-752*ln(5)-864)*x^3+(8*l
n(2)*ln(5)^4+32*ln(2)*ln(5)^3-31*ln(5)^4+96*ln(2)*ln(5)^2-128*ln(5)^3+128*ln(2)*ln(5)-376*ln(5)^2+256*ln(2)-51
2*ln(5)-1008)*x^2)/(2+x)^4/(ln(5)^2+2*x*ln(5)+x^2+4)^2

________________________________________________________________________________________

maxima [B]  time = 0.44, size = 407, normalized size = 14.03 \begin {gather*} \frac {2 \, x^{7} {\left (\log \relax (2) - 4\right )} + {\left (8 \, {\left (\log \relax (2) - 4\right )} \log \relax (5) + 16 \, \log \relax (2) - 63\right )} x^{6} + 4 \, {\left (3 \, {\left (\log \relax (2) - 4\right )} \log \relax (5)^{2} + {\left (12 \, \log \relax (2) - 47\right )} \log \relax (5) + 14 \, \log \relax (2) - 54\right )} x^{5} + 2 \, {\left (4 \, {\left (\log \relax (2) - 4\right )} \log \relax (5)^{3} + {\left (28 \, \log \relax (2) - 109\right )} \log \relax (5)^{2} + 8 \, {\left (8 \, \log \relax (2) - 31\right )} \log \relax (5) + 64 \, \log \relax (2) - 244\right )} x^{4} + 2 \, {\left ({\left (\log \relax (2) - 4\right )} \log \relax (5)^{4} + 2 \, {\left (8 \, \log \relax (2) - 31\right )} \log \relax (5)^{3} + 4 \, {\left (12 \, \log \relax (2) - 47\right )} \log \relax (5)^{2} + 8 \, {\left (12 \, \log \relax (2) - 47\right )} \log \relax (5) + 112 \, \log \relax (2) - 432\right )} x^{3} + {\left ({\left (8 \, \log \relax (2) - 31\right )} \log \relax (5)^{4} + 32 \, {\left (\log \relax (2) - 4\right )} \log \relax (5)^{3} + 8 \, {\left (12 \, \log \relax (2) - 47\right )} \log \relax (5)^{2} + 128 \, {\left (\log \relax (2) - 4\right )} \log \relax (5) + 256 \, \log \relax (2) - 1008\right )} x^{2} + 8 \, {\left ({\left (\log \relax (2) - 4\right )} \log \relax (5)^{4} + 8 \, {\left (\log \relax (2) - 4\right )} \log \relax (5)^{2} + 16 \, \log \relax (2) - 64\right )} x}{x^{8} + 4 \, x^{7} {\left (\log \relax (5) + 2\right )} + 2 \, {\left (3 \, \log \relax (5)^{2} + 16 \, \log \relax (5) + 16\right )} x^{6} + 4 \, {\left (\log \relax (5)^{3} + 12 \, \log \relax (5)^{2} + 28 \, \log \relax (5) + 24\right )} x^{5} + {\left (\log \relax (5)^{4} + 32 \, \log \relax (5)^{3} + 152 \, \log \relax (5)^{2} + 256 \, \log \relax (5) + 224\right )} x^{4} + 8 \, {\left (\log \relax (5)^{4} + 12 \, \log \relax (5)^{3} + 32 \, \log \relax (5)^{2} + 56 \, \log \relax (5) + 48\right )} x^{3} + 16 \, \log \relax (5)^{4} + 8 \, {\left (3 \, \log \relax (5)^{4} + 16 \, \log \relax (5)^{3} + 36 \, \log \relax (5)^{2} + 64 \, \log \relax (5) + 64\right )} x^{2} + 32 \, {\left (\log \relax (5)^{4} + 2 \, \log \relax (5)^{3} + 8 \, \log \relax (5)^{2} + 8 \, \log \relax (5) + 16\right )} x + 128 \, \log \relax (5)^{2} + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^3-4*x^2+8*x+16)*log(2)+8*x^3+14*x^2-28*x-64)*log(5)^6+((-12*x^4-24*x^3+48*x^2+96*x)*log(2)+4
8*x^4+84*x^3-168*x^2-384*x)*log(5)^5+((-30*x^5-60*x^4+128*x^3+320*x^2+224*x+192)*log(2)+120*x^5+210*x^4-460*x^
3-1256*x^2-848*x-768)*log(5)^4+((-40*x^6-96*x^5+96*x^4+448*x^3+768*x^2+768*x)*log(2)+160*x^6+344*x^5-352*x^4-1
728*x^3-2880*x^2-3072*x)*log(5)^3+((-30*x^7-108*x^6-120*x^5+144*x^4+1120*x^3+1984*x^2+1408*x+768)*log(2)+120*x
^7+402*x^6+444*x^5-528*x^4-4128*x^3-7648*x^2-5440*x-3072)*log(5)^2+((-12*x^8-72*x^7-208*x^6-224*x^5+448*x^4+16
64*x^3+2304*x^2+1536*x)*log(2)+48*x^8+276*x^7+776*x^6+832*x^5-1664*x^4-6208*x^3-8832*x^2-6144*x)*log(5)+(-2*x^
9-20*x^8-80*x^7-160*x^6-128*x^5+256*x^4+1280*x^3+2560*x^2+2560*x+1024)*log(2)+8*x^9+78*x^8+300*x^7+568*x^6+432
*x^5-864*x^4-4544*x^3-9600*x^2-9984*x-4096)/((x^5+10*x^4+40*x^3+80*x^2+80*x+32)*log(5)^6+(6*x^6+60*x^5+240*x^4
+480*x^3+480*x^2+192*x)*log(5)^5+(15*x^7+150*x^6+612*x^5+1320*x^4+1680*x^3+1440*x^2+960*x+384)*log(5)^4+(20*x^
8+200*x^7+848*x^6+2080*x^5+3520*x^4+4480*x^3+3840*x^2+1536*x)*log(5)^3+(15*x^9+150*x^8+672*x^7+1920*x^6+4128*x
^5+6720*x^4+7680*x^3+6144*x^2+3840*x+1536)*log(5)^2+(6*x^10+60*x^9+288*x^8+960*x^7+2496*x^6+4992*x^5+7680*x^4+
9216*x^3+7680*x^2+3072*x)*log(5)+x^11+10*x^10+52*x^9+200*x^8+608*x^7+1472*x^6+2944*x^5+4864*x^4+6400*x^3+6656*
x^2+5120*x+2048),x, algorithm="maxima")

[Out]

(2*x^7*(log(2) - 4) + (8*(log(2) - 4)*log(5) + 16*log(2) - 63)*x^6 + 4*(3*(log(2) - 4)*log(5)^2 + (12*log(2) -
47)*log(5) + 14*log(2) - 54)*x^5 + 2*(4*(log(2) - 4)*log(5)^3 + (28*log(2) - 109)*log(5)^2 + 8*(8*log(2) - 31
)*log(5) + 64*log(2) - 244)*x^4 + 2*((log(2) - 4)*log(5)^4 + 2*(8*log(2) - 31)*log(5)^3 + 4*(12*log(2) - 47)*l
og(5)^2 + 8*(12*log(2) - 47)*log(5) + 112*log(2) - 432)*x^3 + ((8*log(2) - 31)*log(5)^4 + 32*(log(2) - 4)*log(
5)^3 + 8*(12*log(2) - 47)*log(5)^2 + 128*(log(2) - 4)*log(5) + 256*log(2) - 1008)*x^2 + 8*((log(2) - 4)*log(5)
^4 + 8*(log(2) - 4)*log(5)^2 + 16*log(2) - 64)*x)/(x^8 + 4*x^7*(log(5) + 2) + 2*(3*log(5)^2 + 16*log(5) + 16)*
x^6 + 4*(log(5)^3 + 12*log(5)^2 + 28*log(5) + 24)*x^5 + (log(5)^4 + 32*log(5)^3 + 152*log(5)^2 + 256*log(5) +
224)*x^4 + 8*(log(5)^4 + 12*log(5)^3 + 32*log(5)^2 + 56*log(5) + 48)*x^3 + 16*log(5)^4 + 8*(3*log(5)^4 + 16*lo
g(5)^3 + 36*log(5)^2 + 64*log(5) + 64)*x^2 + 32*(log(5)^4 + 2*log(5)^3 + 8*log(5)^2 + 8*log(5) + 16)*x + 128*l
og(5)^2 + 256)

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mupad [F(-1)]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \text {Hanged} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(5)*(log(2)*(1536*x + 2304*x^2 + 1664*x^3 + 448*x^4 - 224*x^5 - 208*x^6 - 72*x^7 - 12*x^8) - 6144*x -
8832*x^2 - 6208*x^3 - 1664*x^4 + 832*x^5 + 776*x^6 + 276*x^7 + 48*x^8) - 9984*x - log(5)^4*(848*x + 1256*x^2 +
460*x^3 - 210*x^4 - 120*x^5 - log(2)*(224*x + 320*x^2 + 128*x^3 - 60*x^4 - 30*x^5 + 192) + 768) + log(5)^6*(l
og(2)*(8*x - 4*x^2 - 2*x^3 + 16) - 28*x + 14*x^2 + 8*x^3 - 64) - log(5)^3*(3072*x - log(2)*(768*x + 768*x^2 +
448*x^3 + 96*x^4 - 96*x^5 - 40*x^6) + 2880*x^2 + 1728*x^3 + 352*x^4 - 344*x^5 - 160*x^6) + log(5)^5*(log(2)*(9
6*x + 48*x^2 - 24*x^3 - 12*x^4) - 384*x - 168*x^2 + 84*x^3 + 48*x^4) + log(2)*(2560*x + 2560*x^2 + 1280*x^3 +
256*x^4 - 128*x^5 - 160*x^6 - 80*x^7 - 20*x^8 - 2*x^9 + 1024) - 9600*x^2 - 4544*x^3 - 864*x^4 + 432*x^5 + 568*
x^6 + 300*x^7 + 78*x^8 + 8*x^9 - log(5)^2*(5440*x - log(2)*(1408*x + 1984*x^2 + 1120*x^3 + 144*x^4 - 120*x^5 -
108*x^6 - 30*x^7 + 768) + 7648*x^2 + 4128*x^3 + 528*x^4 - 444*x^5 - 402*x^6 - 120*x^7 + 3072) - 4096)/(5120*x
+ log(5)^2*(3840*x + 6144*x^2 + 7680*x^3 + 6720*x^4 + 4128*x^5 + 1920*x^6 + 672*x^7 + 150*x^8 + 15*x^9 + 1536
) + log(5)^5*(192*x + 480*x^2 + 480*x^3 + 240*x^4 + 60*x^5 + 6*x^6) + log(5)^4*(960*x + 1440*x^2 + 1680*x^3 +
1320*x^4 + 612*x^5 + 150*x^6 + 15*x^7 + 384) + 6656*x^2 + 6400*x^3 + 4864*x^4 + 2944*x^5 + 1472*x^6 + 608*x^7
+ 200*x^8 + 52*x^9 + 10*x^10 + x^11 + log(5)^6*(80*x + 80*x^2 + 40*x^3 + 10*x^4 + x^5 + 32) + log(5)^3*(1536*x
+ 3840*x^2 + 4480*x^3 + 3520*x^4 + 2080*x^5 + 848*x^6 + 200*x^7 + 20*x^8) + log(5)*(3072*x + 7680*x^2 + 9216*
x^3 + 7680*x^4 + 4992*x^5 + 2496*x^6 + 960*x^7 + 288*x^8 + 60*x^9 + 6*x^10) + 2048),x)

[Out]

\text{Hanged}

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x**3-4*x**2+8*x+16)*ln(2)+8*x**3+14*x**2-28*x-64)*ln(5)**6+((-12*x**4-24*x**3+48*x**2+96*x)*ln
(2)+48*x**4+84*x**3-168*x**2-384*x)*ln(5)**5+((-30*x**5-60*x**4+128*x**3+320*x**2+224*x+192)*ln(2)+120*x**5+21
0*x**4-460*x**3-1256*x**2-848*x-768)*ln(5)**4+((-40*x**6-96*x**5+96*x**4+448*x**3+768*x**2+768*x)*ln(2)+160*x*
*6+344*x**5-352*x**4-1728*x**3-2880*x**2-3072*x)*ln(5)**3+((-30*x**7-108*x**6-120*x**5+144*x**4+1120*x**3+1984
*x**2+1408*x+768)*ln(2)+120*x**7+402*x**6+444*x**5-528*x**4-4128*x**3-7648*x**2-5440*x-3072)*ln(5)**2+((-12*x*
*8-72*x**7-208*x**6-224*x**5+448*x**4+1664*x**3+2304*x**2+1536*x)*ln(2)+48*x**8+276*x**7+776*x**6+832*x**5-166
4*x**4-6208*x**3-8832*x**2-6144*x)*ln(5)+(-2*x**9-20*x**8-80*x**7-160*x**6-128*x**5+256*x**4+1280*x**3+2560*x*
*2+2560*x+1024)*ln(2)+8*x**9+78*x**8+300*x**7+568*x**6+432*x**5-864*x**4-4544*x**3-9600*x**2-9984*x-4096)/((x*
*5+10*x**4+40*x**3+80*x**2+80*x+32)*ln(5)**6+(6*x**6+60*x**5+240*x**4+480*x**3+480*x**2+192*x)*ln(5)**5+(15*x*
*7+150*x**6+612*x**5+1320*x**4+1680*x**3+1440*x**2+960*x+384)*ln(5)**4+(20*x**8+200*x**7+848*x**6+2080*x**5+35
20*x**4+4480*x**3+3840*x**2+1536*x)*ln(5)**3+(15*x**9+150*x**8+672*x**7+1920*x**6+4128*x**5+6720*x**4+7680*x**
3+6144*x**2+3840*x+1536)*ln(5)**2+(6*x**10+60*x**9+288*x**8+960*x**7+2496*x**6+4992*x**5+7680*x**4+9216*x**3+7
680*x**2+3072*x)*ln(5)+x**11+10*x**10+52*x**9+200*x**8+608*x**7+1472*x**6+2944*x**5+4864*x**4+6400*x**3+6656*x
**2+5120*x+2048),x)

[Out]

Timed out

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