3.32.32 \(\int \frac {-950+170 x+2205 x^2+2184 x^3+1014 x^4+258 x^5+35 x^6+2 x^7+(1770-830 x-3792 x^2-2904 x^3-1014 x^4-174 x^5-12 x^6) \log (4)+(-1375+1032 x+2628 x^2+1476 x^3+345 x^4+30 x^5) \log ^2(4)+(576-600 x-924 x^2-340 x^3-40 x^4) \log ^3(4)+(-138+186 x+165 x^2+30 x^3) \log ^4(4)+(18-30 x-12 x^2) \log ^5(4)+(-1+2 x) \log ^6(4)}{-950 x-770 x^2+425 x^3+804 x^4+438 x^5+120 x^6+17 x^7+x^8+(1770 x+950 x^2-1032 x^3-1176 x^4-462 x^5-84 x^6-6 x^7) \log (4)+(-1375 x-348 x^2+900 x^3+648 x^4+165 x^5+15 x^6) \log ^2(4)+(576 x-24 x^2-372 x^3-160 x^4-20 x^5) \log ^3(4)+(-138 x+48 x^2+75 x^3+15 x^4) \log ^4(4)+(18 x-12 x^2-6 x^3) \log ^5(4)+(-x+x^2) \log ^6(4)} \, dx\)

Optimal. Leaf size=22 \[ \log (x)+\log \left (-1+x+\frac {5}{\left (1+(3+x-\log (4))^2\right )^2}\right ) \]

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Rubi [B]  time = 1.17, antiderivative size = 129, normalized size of antiderivative = 5.86, number of steps used = 4, number of rules used = 3, integrand size = 363, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2074, 628, 1587} \begin {gather*} -2 \log \left (x^2+2 x (3-\log (4))+10+\log ^2(4)-6 \log (4)\right )+\log \left (x^5+x^4 (11-8 \log (2))+4 x^3 (11-\log (4) (8-\log (8)))+2 x^2 \left (32+\log ^2(4) (15-\log (16))-38 \log (4)\right )-2 x \left (10+\log (4) \left (4+(4-\log (2)) \log ^2(4)-10 \log (4)\right )\right )-95+2 \log (4) \left (60+(6-\log (2)) \log ^2(4)-28 \log (4)\right )\right )+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-950 + 170*x + 2205*x^2 + 2184*x^3 + 1014*x^4 + 258*x^5 + 35*x^6 + 2*x^7 + (1770 - 830*x - 3792*x^2 - 290
4*x^3 - 1014*x^4 - 174*x^5 - 12*x^6)*Log[4] + (-1375 + 1032*x + 2628*x^2 + 1476*x^3 + 345*x^4 + 30*x^5)*Log[4]
^2 + (576 - 600*x - 924*x^2 - 340*x^3 - 40*x^4)*Log[4]^3 + (-138 + 186*x + 165*x^2 + 30*x^3)*Log[4]^4 + (18 -
30*x - 12*x^2)*Log[4]^5 + (-1 + 2*x)*Log[4]^6)/(-950*x - 770*x^2 + 425*x^3 + 804*x^4 + 438*x^5 + 120*x^6 + 17*
x^7 + x^8 + (1770*x + 950*x^2 - 1032*x^3 - 1176*x^4 - 462*x^5 - 84*x^6 - 6*x^7)*Log[4] + (-1375*x - 348*x^2 +
900*x^3 + 648*x^4 + 165*x^5 + 15*x^6)*Log[4]^2 + (576*x - 24*x^2 - 372*x^3 - 160*x^4 - 20*x^5)*Log[4]^3 + (-13
8*x + 48*x^2 + 75*x^3 + 15*x^4)*Log[4]^4 + (18*x - 12*x^2 - 6*x^3)*Log[4]^5 + (-x + x^2)*Log[4]^6),x]

[Out]

Log[x] - 2*Log[10 + x^2 + 2*x*(3 - Log[4]) - 6*Log[4] + Log[4]^2] + Log[-95 + x^5 + x^4*(11 - 8*Log[2]) + 2*Lo
g[4]*(60 - 28*Log[4] + (6 - Log[2])*Log[4]^2) - 2*x*(10 + Log[4]*(4 - 10*Log[4] + (4 - Log[2])*Log[4]^2)) + 4*
x^3*(11 - Log[4]*(8 - Log[8])) + 2*x^2*(32 - 38*Log[4] + Log[4]^2*(15 - Log[16]))]

Rule 628

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

Rule 1587

Int[(Pp_)/(Qq_), x_Symbol] :> With[{p = Expon[Pp, x], q = Expon[Qq, x]}, Simp[(Coeff[Pp, x, p]*Log[RemoveConte
nt[Qq, x]])/(q*Coeff[Qq, x, q]), x] /; EqQ[p, q - 1] && EqQ[Pp, Simplify[(Coeff[Pp, x, p]*D[Qq, x])/(q*Coeff[Q
q, x, q])]]] /; PolyQ[Pp, x] && PolyQ[Qq, x]

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 {1}{x}+\frac {4 (-3-x+\log (4))}{10+x^2+2 x (3-\log (4))-6 \log (4)+\log ^2(4)}+\frac {5 x^4+4 x^3 (11-4 \log (4))-\left (2+2 \log (4)-\log ^2(4)\right ) \left (10-6 \log (4)+\log ^2(4)\right )+4 x (2-\log (4)) \left (16-11 \log (4)+2 \log ^2(4)\right )+6 x^2 \left (22-16 \log (4)+3 \log ^2(4)\right )}{x^5+11 x^4 \left (1-\frac {8 \log (2)}{11}\right )-95 \left (1+\frac {2}{95} \log (4) \left (-60+28 \log (4)+(-6+\log (2)) \log ^2(4)\right )\right )-20 x \left (1+\frac {2}{5} \log (4) \left (1-\frac {1}{4} \log (4) (10+(-4+\log (2)) \log (4))\right )\right )+44 x^3 \left (1+\frac {1}{11} \log (4) (-8+\log (8))\right )+64 x^2 \left (1-\frac {1}{32} \log (4) (38+\log (4) (-15+\log (16)))\right )}\right ) \, dx\\ &=\log (x)+4 \int \frac {-3-x+\log (4)}{10+x^2+2 x (3-\log (4))-6 \log (4)+\log ^2(4)} \, dx+\int \frac {5 x^4+4 x^3 (11-4 \log (4))-\left (2+2 \log (4)-\log ^2(4)\right ) \left (10-6 \log (4)+\log ^2(4)\right )+4 x (2-\log (4)) \left (16-11 \log (4)+2 \log ^2(4)\right )+6 x^2 \left (22-16 \log (4)+3 \log ^2(4)\right )}{x^5+11 x^4 \left (1-\frac {8 \log (2)}{11}\right )-95 \left (1+\frac {2}{95} \log (4) \left (-60+28 \log (4)+(-6+\log (2)) \log ^2(4)\right )\right )-20 x \left (1+\frac {2}{5} \log (4) \left (1-\frac {1}{4} \log (4) (10+(-4+\log (2)) \log (4))\right )\right )+44 x^3 \left (1+\frac {1}{11} \log (4) (-8+\log (8))\right )+64 x^2 \left (1-\frac {1}{32} \log (4) (38+\log (4) (-15+\log (16)))\right )} \, dx\\ &=\log (x)-2 \log \left (10+x^2+2 x (3-\log (4))-6 \log (4)+\log ^2(4)\right )+\log \left (-95+x^5+x^4 (11-8 \log (2))+2 \log (4) \left (60-28 \log (4)+(6-\log (2)) \log ^2(4)\right )-2 x (10+\log (4) (4-\log (4) (10-(4-\log (2)) \log (4))))+4 x^3 (11-\log (4) (8-\log (8)))+2 x^2 (32-\log (4) (38-\log (4) (15-\log (16))))\right )\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.22, size = 147, normalized size = 6.68 \begin {gather*} \log (x)-2 \log \left (10+6 x+x^2-6 \log (4)-2 x \log (4)+\log ^2(4)\right )+\log \left (95+20 x-64 x^2-44 x^3-11 x^4-x^5-120 \log (4)+8 x \log (4)+76 x^2 \log (4)+32 x^3 \log (4)+4 x^4 \log (4)+56 \log ^2(4)-20 x \log ^2(4)-30 x^2 \log ^2(4)-6 x^3 \log ^2(4)-12 \log ^3(4)+8 x \log ^3(4)+4 x^2 \log ^3(4)+\log ^4(4)-x \log ^4(4)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-950 + 170*x + 2205*x^2 + 2184*x^3 + 1014*x^4 + 258*x^5 + 35*x^6 + 2*x^7 + (1770 - 830*x - 3792*x^2
- 2904*x^3 - 1014*x^4 - 174*x^5 - 12*x^6)*Log[4] + (-1375 + 1032*x + 2628*x^2 + 1476*x^3 + 345*x^4 + 30*x^5)*
Log[4]^2 + (576 - 600*x - 924*x^2 - 340*x^3 - 40*x^4)*Log[4]^3 + (-138 + 186*x + 165*x^2 + 30*x^3)*Log[4]^4 +
(18 - 30*x - 12*x^2)*Log[4]^5 + (-1 + 2*x)*Log[4]^6)/(-950*x - 770*x^2 + 425*x^3 + 804*x^4 + 438*x^5 + 120*x^6
+ 17*x^7 + x^8 + (1770*x + 950*x^2 - 1032*x^3 - 1176*x^4 - 462*x^5 - 84*x^6 - 6*x^7)*Log[4] + (-1375*x - 348*
x^2 + 900*x^3 + 648*x^4 + 165*x^5 + 15*x^6)*Log[4]^2 + (576*x - 24*x^2 - 372*x^3 - 160*x^4 - 20*x^5)*Log[4]^3
+ (-138*x + 48*x^2 + 75*x^3 + 15*x^4)*Log[4]^4 + (18*x - 12*x^2 - 6*x^3)*Log[4]^5 + (-x + x^2)*Log[4]^6),x]

[Out]

Log[x] - 2*Log[10 + 6*x + x^2 - 6*Log[4] - 2*x*Log[4] + Log[4]^2] + Log[95 + 20*x - 64*x^2 - 44*x^3 - 11*x^4 -
x^5 - 120*Log[4] + 8*x*Log[4] + 76*x^2*Log[4] + 32*x^3*Log[4] + 4*x^4*Log[4] + 56*Log[4]^2 - 20*x*Log[4]^2 -
30*x^2*Log[4]^2 - 6*x^3*Log[4]^2 - 12*Log[4]^3 + 8*x*Log[4]^3 + 4*x^2*Log[4]^3 + Log[4]^4 - x*Log[4]^4]

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fricas [B]  time = 0.67, size = 135, normalized size = 6.14 \begin {gather*} \log \left (x^{6} + 11 \, x^{5} + 16 \, {\left (x^{2} - x\right )} \log \relax (2)^{4} + 44 \, x^{4} - 32 \, {\left (x^{3} + 2 \, x^{2} - 3 \, x\right )} \log \relax (2)^{3} + 64 \, x^{3} + 8 \, {\left (3 \, x^{4} + 15 \, x^{3} + 10 \, x^{2} - 28 \, x\right )} \log \relax (2)^{2} - 20 \, x^{2} - 8 \, {\left (x^{5} + 8 \, x^{4} + 19 \, x^{3} + 2 \, x^{2} - 30 \, x\right )} \log \relax (2) - 95 \, x\right ) - 2 \, \log \left (x^{2} - 4 \, {\left (x + 3\right )} \log \relax (2) + 4 \, \log \relax (2)^{2} + 6 \, x + 10\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((64*(2*x-1)*log(2)^6+32*(-12*x^2-30*x+18)*log(2)^5+16*(30*x^3+165*x^2+186*x-138)*log(2)^4+8*(-40*x^4
-340*x^3-924*x^2-600*x+576)*log(2)^3+4*(30*x^5+345*x^4+1476*x^3+2628*x^2+1032*x-1375)*log(2)^2+2*(-12*x^6-174*
x^5-1014*x^4-2904*x^3-3792*x^2-830*x+1770)*log(2)+2*x^7+35*x^6+258*x^5+1014*x^4+2184*x^3+2205*x^2+170*x-950)/(
64*(x^2-x)*log(2)^6+32*(-6*x^3-12*x^2+18*x)*log(2)^5+16*(15*x^4+75*x^3+48*x^2-138*x)*log(2)^4+8*(-20*x^5-160*x
^4-372*x^3-24*x^2+576*x)*log(2)^3+4*(15*x^6+165*x^5+648*x^4+900*x^3-348*x^2-1375*x)*log(2)^2+2*(-6*x^7-84*x^6-
462*x^5-1176*x^4-1032*x^3+950*x^2+1770*x)*log(2)+x^8+17*x^7+120*x^6+438*x^5+804*x^4+425*x^3-770*x^2-950*x),x,
algorithm="fricas")

[Out]

log(x^6 + 11*x^5 + 16*(x^2 - x)*log(2)^4 + 44*x^4 - 32*(x^3 + 2*x^2 - 3*x)*log(2)^3 + 64*x^3 + 8*(3*x^4 + 15*x
^3 + 10*x^2 - 28*x)*log(2)^2 - 20*x^2 - 8*(x^5 + 8*x^4 + 19*x^3 + 2*x^2 - 30*x)*log(2) - 95*x) - 2*log(x^2 - 4
*(x + 3)*log(2) + 4*log(2)^2 + 6*x + 10)

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giac [B]  time = 0.56, size = 151, normalized size = 6.86 \begin {gather*} -2 \, \log \left (x^{2} - 4 \, x \log \relax (2) + 4 \, \log \relax (2)^{2} + 6 \, x - 12 \, \log \relax (2) + 10\right ) + \log \left ({\left | x^{5} - 8 \, x^{4} \log \relax (2) + 24 \, x^{3} \log \relax (2)^{2} - 32 \, x^{2} \log \relax (2)^{3} + 16 \, x \log \relax (2)^{4} + 11 \, x^{4} - 64 \, x^{3} \log \relax (2) + 120 \, x^{2} \log \relax (2)^{2} - 64 \, x \log \relax (2)^{3} - 16 \, \log \relax (2)^{4} + 44 \, x^{3} - 152 \, x^{2} \log \relax (2) + 80 \, x \log \relax (2)^{2} + 96 \, \log \relax (2)^{3} + 64 \, x^{2} - 16 \, x \log \relax (2) - 224 \, \log \relax (2)^{2} - 20 \, x + 240 \, \log \relax (2) - 95 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((64*(2*x-1)*log(2)^6+32*(-12*x^2-30*x+18)*log(2)^5+16*(30*x^3+165*x^2+186*x-138)*log(2)^4+8*(-40*x^4
-340*x^3-924*x^2-600*x+576)*log(2)^3+4*(30*x^5+345*x^4+1476*x^3+2628*x^2+1032*x-1375)*log(2)^2+2*(-12*x^6-174*
x^5-1014*x^4-2904*x^3-3792*x^2-830*x+1770)*log(2)+2*x^7+35*x^6+258*x^5+1014*x^4+2184*x^3+2205*x^2+170*x-950)/(
64*(x^2-x)*log(2)^6+32*(-6*x^3-12*x^2+18*x)*log(2)^5+16*(15*x^4+75*x^3+48*x^2-138*x)*log(2)^4+8*(-20*x^5-160*x
^4-372*x^3-24*x^2+576*x)*log(2)^3+4*(15*x^6+165*x^5+648*x^4+900*x^3-348*x^2-1375*x)*log(2)^2+2*(-6*x^7-84*x^6-
462*x^5-1176*x^4-1032*x^3+950*x^2+1770*x)*log(2)+x^8+17*x^7+120*x^6+438*x^5+804*x^4+425*x^3-770*x^2-950*x),x,
algorithm="giac")

[Out]

-2*log(x^2 - 4*x*log(2) + 4*log(2)^2 + 6*x - 12*log(2) + 10) + log(abs(x^5 - 8*x^4*log(2) + 24*x^3*log(2)^2 -
32*x^2*log(2)^3 + 16*x*log(2)^4 + 11*x^4 - 64*x^3*log(2) + 120*x^2*log(2)^2 - 64*x*log(2)^3 - 16*log(2)^4 + 44
*x^3 - 152*x^2*log(2) + 80*x*log(2)^2 + 96*log(2)^3 + 64*x^2 - 16*x*log(2) - 224*log(2)^2 - 20*x + 240*log(2)
- 95)) + log(abs(x))

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maple [B]  time = 0.39, size = 137, normalized size = 6.23

method	result	size
risch	\(-2 \ln \left (-x^{2}+\left (4 \ln \relax (2)-6\right ) x -4 \ln \relax (2)^{2}+12 \ln \relax (2)-10\right )+\ln \left (x^{6}+\left (-8 \ln \relax (2)+11\right ) x^{5}+\left (24 \ln \relax (2)^{2}-64 \ln \relax (2)+44\right ) x^{4}+\left (-32 \ln \relax (2)^{3}+120 \ln \relax (2)^{2}-152 \ln \relax (2)+64\right ) x^{3}+\left (16 \ln \relax (2)^{4}-64 \ln \relax (2)^{3}+80 \ln \relax (2)^{2}-16 \ln \relax (2)-20\right ) x^{2}+\left (-16 \ln \relax (2)^{4}+96 \ln \relax (2)^{3}-224 \ln \relax (2)^{2}+240 \ln \relax (2)-95\right ) x \right )\)	\(137\)
default	\(\ln \relax (x )+\ln \left (16 x \ln \relax (2)^{4}-32 x^{2} \ln \relax (2)^{3}+24 x^{3} \ln \relax (2)^{2}-8 x^{4} \ln \relax (2)+x^{5}-16 \ln \relax (2)^{4}-64 x \ln \relax (2)^{3}+120 x^{2} \ln \relax (2)^{2}-64 x^{3} \ln \relax (2)+11 x^{4}+96 \ln \relax (2)^{3}+80 x \ln \relax (2)^{2}-152 x^{2} \ln \relax (2)+44 x^{3}-224 \ln \relax (2)^{2}-16 x \ln \relax (2)+64 x^{2}+240 \ln \relax (2)-20 x -95\right )-2 \ln \left (4 \ln \relax (2)^{2}-4 x \ln \relax (2)+x^{2}-12 \ln \relax (2)+6 x +10\right )\)	\(150\)
norman	\(\ln \relax (x )+\ln \left (16 x \ln \relax (2)^{4}-32 x^{2} \ln \relax (2)^{3}+24 x^{3} \ln \relax (2)^{2}-8 x^{4} \ln \relax (2)+x^{5}-16 \ln \relax (2)^{4}-64 x \ln \relax (2)^{3}+120 x^{2} \ln \relax (2)^{2}-64 x^{3} \ln \relax (2)+11 x^{4}+96 \ln \relax (2)^{3}+80 x \ln \relax (2)^{2}-152 x^{2} \ln \relax (2)+44 x^{3}-224 \ln \relax (2)^{2}-16 x \ln \relax (2)+64 x^{2}+240 \ln \relax (2)-20 x -95\right )-2 \ln \left (4 \ln \relax (2)^{2}-4 x \ln \relax (2)+x^{2}-12 \ln \relax (2)+6 x +10\right )\)	\(150\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((64*(2*x-1)*ln(2)^6+32*(-12*x^2-30*x+18)*ln(2)^5+16*(30*x^3+165*x^2+186*x-138)*ln(2)^4+8*(-40*x^4-340*x^3-
924*x^2-600*x+576)*ln(2)^3+4*(30*x^5+345*x^4+1476*x^3+2628*x^2+1032*x-1375)*ln(2)^2+2*(-12*x^6-174*x^5-1014*x^
4-2904*x^3-3792*x^2-830*x+1770)*ln(2)+2*x^7+35*x^6+258*x^5+1014*x^4+2184*x^3+2205*x^2+170*x-950)/(64*(x^2-x)*l
n(2)^6+32*(-6*x^3-12*x^2+18*x)*ln(2)^5+16*(15*x^4+75*x^3+48*x^2-138*x)*ln(2)^4+8*(-20*x^5-160*x^4-372*x^3-24*x
^2+576*x)*ln(2)^3+4*(15*x^6+165*x^5+648*x^4+900*x^3-348*x^2-1375*x)*ln(2)^2+2*(-6*x^7-84*x^6-462*x^5-1176*x^4-
1032*x^3+950*x^2+1770*x)*ln(2)+x^8+17*x^7+120*x^6+438*x^5+804*x^4+425*x^3-770*x^2-950*x),x,method=_RETURNVERBO
SE)

[Out]

-2*ln(-x^2+(4*ln(2)-6)*x-4*ln(2)^2+12*ln(2)-10)+ln(x^6+(-8*ln(2)+11)*x^5+(24*ln(2)^2-64*ln(2)+44)*x^4+(-32*ln(
2)^3+120*ln(2)^2-152*ln(2)+64)*x^3+(16*ln(2)^4-64*ln(2)^3+80*ln(2)^2-16*ln(2)-20)*x^2+(-16*ln(2)^4+96*ln(2)^3-
224*ln(2)^2+240*ln(2)-95)*x)

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maxima [B]  time = 0.92, size = 136, normalized size = 6.18 \begin {gather*} \log \left (x^{5} - x^{4} {\left (8 \, \log \relax (2) - 11\right )} + 4 \, {\left (6 \, \log \relax (2)^{2} - 16 \, \log \relax (2) + 11\right )} x^{3} - 16 \, \log \relax (2)^{4} - 8 \, {\left (4 \, \log \relax (2)^{3} - 15 \, \log \relax (2)^{2} + 19 \, \log \relax (2) - 8\right )} x^{2} + 96 \, \log \relax (2)^{3} + 4 \, {\left (4 \, \log \relax (2)^{4} - 16 \, \log \relax (2)^{3} + 20 \, \log \relax (2)^{2} - 4 \, \log \relax (2) - 5\right )} x - 224 \, \log \relax (2)^{2} + 240 \, \log \relax (2) - 95\right ) - 2 \, \log \left (x^{2} - 2 \, x {\left (2 \, \log \relax (2) - 3\right )} + 4 \, \log \relax (2)^{2} - 12 \, \log \relax (2) + 10\right ) + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((64*(2*x-1)*log(2)^6+32*(-12*x^2-30*x+18)*log(2)^5+16*(30*x^3+165*x^2+186*x-138)*log(2)^4+8*(-40*x^4
-340*x^3-924*x^2-600*x+576)*log(2)^3+4*(30*x^5+345*x^4+1476*x^3+2628*x^2+1032*x-1375)*log(2)^2+2*(-12*x^6-174*
x^5-1014*x^4-2904*x^3-3792*x^2-830*x+1770)*log(2)+2*x^7+35*x^6+258*x^5+1014*x^4+2184*x^3+2205*x^2+170*x-950)/(
64*(x^2-x)*log(2)^6+32*(-6*x^3-12*x^2+18*x)*log(2)^5+16*(15*x^4+75*x^3+48*x^2-138*x)*log(2)^4+8*(-20*x^5-160*x
^4-372*x^3-24*x^2+576*x)*log(2)^3+4*(15*x^6+165*x^5+648*x^4+900*x^3-348*x^2-1375*x)*log(2)^2+2*(-6*x^7-84*x^6-
462*x^5-1176*x^4-1032*x^3+950*x^2+1770*x)*log(2)+x^8+17*x^7+120*x^6+438*x^5+804*x^4+425*x^3-770*x^2-950*x),x,
algorithm="maxima")

[Out]

log(x^5 - x^4*(8*log(2) - 11) + 4*(6*log(2)^2 - 16*log(2) + 11)*x^3 - 16*log(2)^4 - 8*(4*log(2)^3 - 15*log(2)^
2 + 19*log(2) - 8)*x^2 + 96*log(2)^3 + 4*(4*log(2)^4 - 16*log(2)^3 + 20*log(2)^2 - 4*log(2) - 5)*x - 224*log(2
)^2 + 240*log(2) - 95) - 2*log(x^2 - 2*x*(2*log(2) - 3) + 4*log(2)^2 - 12*log(2) + 10) + log(x)

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mupad [B]  time = 3.11, size = 151, normalized size = 6.86 \begin {gather*} \ln \left (x\,\left (20\,x-240\,\ln \relax (2)-120\,x^2\,{\ln \relax (2)}^2+32\,x^2\,{\ln \relax (2)}^3-24\,x^3\,{\ln \relax (2)}^2+16\,x\,\ln \relax (2)-80\,x\,{\ln \relax (2)}^2+152\,x^2\,\ln \relax (2)+64\,x\,{\ln \relax (2)}^3+64\,x^3\,\ln \relax (2)-16\,x\,{\ln \relax (2)}^4+8\,x^4\,\ln \relax (2)+224\,{\ln \relax (2)}^2-96\,{\ln \relax (2)}^3+16\,{\ln \relax (2)}^4-64\,x^2-44\,x^3-11\,x^4-x^5+95\right )\right )-2\,\ln \left (6\,x-12\,\ln \relax (2)-4\,x\,\ln \relax (2)+4\,{\ln \relax (2)}^2+x^2+10\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((170*x - 8*log(2)^3*(600*x + 924*x^2 + 340*x^3 + 40*x^4 - 576) - 2*log(2)*(830*x + 3792*x^2 + 2904*x^3 + 1
014*x^4 + 174*x^5 + 12*x^6 - 1770) + 4*log(2)^2*(1032*x + 2628*x^2 + 1476*x^3 + 345*x^4 + 30*x^5 - 1375) + 64*
log(2)^6*(2*x - 1) - 32*log(2)^5*(30*x + 12*x^2 - 18) + 16*log(2)^4*(186*x + 165*x^2 + 30*x^3 - 138) + 2205*x^
2 + 2184*x^3 + 1014*x^4 + 258*x^5 + 35*x^6 + 2*x^7 - 950)/(16*log(2)^4*(48*x^2 - 138*x + 75*x^3 + 15*x^4) - 95
0*x - 64*log(2)^6*(x - x^2) - 8*log(2)^3*(24*x^2 - 576*x + 372*x^3 + 160*x^4 + 20*x^5) - 2*log(2)*(1032*x^3 -
950*x^2 - 1770*x + 1176*x^4 + 462*x^5 + 84*x^6 + 6*x^7) + 4*log(2)^2*(900*x^3 - 348*x^2 - 1375*x + 648*x^4 + 1
65*x^5 + 15*x^6) - 32*log(2)^5*(12*x^2 - 18*x + 6*x^3) - 770*x^2 + 425*x^3 + 804*x^4 + 438*x^5 + 120*x^6 + 17*
x^7 + x^8),x)

[Out]

log(x*(20*x - 240*log(2) - 120*x^2*log(2)^2 + 32*x^2*log(2)^3 - 24*x^3*log(2)^2 + 16*x*log(2) - 80*x*log(2)^2
+ 152*x^2*log(2) + 64*x*log(2)^3 + 64*x^3*log(2) - 16*x*log(2)^4 + 8*x^4*log(2) + 224*log(2)^2 - 96*log(2)^3 +
16*log(2)^4 - 64*x^2 - 44*x^3 - 11*x^4 - x^5 + 95)) - 2*log(6*x - 12*log(2) - 4*x*log(2) + 4*log(2)^2 + x^2 +
10)

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sympy [B]  time = 16.56, size = 143, normalized size = 6.50 \begin {gather*} - 2 \log {\left (x^{2} + x \left (6 - 4 \log {\relax (2 )}\right ) - 12 \log {\relax (2 )} + 4 \log {\relax (2 )}^{2} + 10 \right )} + \log {\left (x^{6} + x^{5} \left (11 - 8 \log {\relax (2 )}\right ) + x^{4} \left (- 64 \log {\relax (2 )} + 24 \log {\relax (2 )}^{2} + 44\right ) + x^{3} \left (- 152 \log {\relax (2 )} - 32 \log {\relax (2 )}^{3} + 120 \log {\relax (2 )}^{2} + 64\right ) + x^{2} \left (- 64 \log {\relax (2 )}^{3} - 20 - 16 \log {\relax (2 )} + 16 \log {\relax (2 )}^{4} + 80 \log {\relax (2 )}^{2}\right ) + x \left (- 224 \log {\relax (2 )}^{2} - 95 - 16 \log {\relax (2 )}^{4} + 96 \log {\relax (2 )}^{3} + 240 \log {\relax (2 )}\right ) \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((64*(2*x-1)*ln(2)**6+32*(-12*x**2-30*x+18)*ln(2)**5+16*(30*x**3+165*x**2+186*x-138)*ln(2)**4+8*(-40*
x**4-340*x**3-924*x**2-600*x+576)*ln(2)**3+4*(30*x**5+345*x**4+1476*x**3+2628*x**2+1032*x-1375)*ln(2)**2+2*(-1
2*x**6-174*x**5-1014*x**4-2904*x**3-3792*x**2-830*x+1770)*ln(2)+2*x**7+35*x**6+258*x**5+1014*x**4+2184*x**3+22
05*x**2+170*x-950)/(64*(x**2-x)*ln(2)**6+32*(-6*x**3-12*x**2+18*x)*ln(2)**5+16*(15*x**4+75*x**3+48*x**2-138*x)
*ln(2)**4+8*(-20*x**5-160*x**4-372*x**3-24*x**2+576*x)*ln(2)**3+4*(15*x**6+165*x**5+648*x**4+900*x**3-348*x**2
-1375*x)*ln(2)**2+2*(-6*x**7-84*x**6-462*x**5-1176*x**4-1032*x**3+950*x**2+1770*x)*ln(2)+x**8+17*x**7+120*x**6
+438*x**5+804*x**4+425*x**3-770*x**2-950*x),x)

[Out]

-2*log(x**2 + x*(6 - 4*log(2)) - 12*log(2) + 4*log(2)**2 + 10) + log(x**6 + x**5*(11 - 8*log(2)) + x**4*(-64*l
og(2) + 24*log(2)**2 + 44) + x**3*(-152*log(2) - 32*log(2)**3 + 120*log(2)**2 + 64) + x**2*(-64*log(2)**3 - 20
- 16*log(2) + 16*log(2)**4 + 80*log(2)**2) + x*(-224*log(2)**2 - 95 - 16*log(2)**4 + 96*log(2)**3 + 240*log(2
)))

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