∫ −32+32x2+(−32+32x) log(3)+(16x3−16x4) log(1+x+log(3))+(24x2−8x3−32x4+(24x2−32x3) log(3)) log2(1+x+log(3))+4x6 log3(1+x+log(3))+(6x5+6x6+6x5 log(3)) log4(1+x+log(3))___________________________________________________________________________________________________________________________________

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

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Rubi [A]
time = 0.19, antiderivative size = 19, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 3, integrand size = 120, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6820, 12, 6818} \begin {gather*} \left (x^3 \log ^2(x+1+\log (3))-4 x+4\right )^2 \end {gather*}

Int[(-32 + 32*x^2 + (-32 + 32*x)*Log[3] + (16*x^3 - 16*x^4)*Log[1 + x + Log[3]] + (24*x^2 - 8*x^3 - 32*x^4 + (

24*x^2 - 32*x^3)*Log[3])*Log[1 + x + Log[3]]^2 + 4*x^6*Log[1 + x + Log[3]]^3 + (6*x^5 + 6*x^6 + 6*x^5*Log[3])*

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

Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[q*(y^(m + 1)/(m + 1)), x] /; !F

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

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

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Mathematica [A]
time = 0.04, size = 19, normalized size = 0.68 \begin {gather*} \left (4-4 x+x^3 \log ^2(1+x+\log (3))\right )^2 \end {gather*}

Integrate[(-32 + 32*x^2 + (-32 + 32*x)*Log[3] + (16*x^3 - 16*x^4)*Log[1 + x + Log[3]] + (24*x^2 - 8*x^3 - 32*x

^4 + (24*x^2 - 32*x^3)*Log[3])*Log[1 + x + Log[3]]^2 + 4*x^6*Log[1 + x + Log[3]]^3 + (6*x^5 + 6*x^6 + 6*x^5*Lo

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(2872\) vs. \(2(28)=56\).
time = 1.86, size = 2873, normalized size = 102.61


method	result	size

risch	\(\ln \left (x +\ln \left (3\right )+1\right )^{4} x^{6}+\left (-8 x^{4}+8 x^{3}\right ) \ln \left (x +\ln \left (3\right )+1\right )^{2}+16 x^{2}-32 x\)	\(42\)
derivativedivides	\(\text {Expression too large to display}\)	\(2873\)
default	\(\text {Expression too large to display}\)	\(2873\)

int(((6*x^5*ln(3)+6*x^6+6*x^5)*ln(x+ln(3)+1)^4+4*x^6*ln(x+ln(3)+1)^3+((-32*x^3+24*x^2)*ln(3)-32*x^4-8*x^3+24*x

^2)*ln(x+ln(3)+1)^2+(-16*x^4+16*x^3)*ln(x+ln(3)+1)+(32*x-32)*ln(3)+32*x^2-32)/(x+ln(3)+1),x,method=_RETURNVERB

-64-64*x+16*(x+ln(3)+1)^2-64*ln(3)+64*ln(3)*(1/3*ln(x+ln(3)+1)*(x+ln(3)+1)^3-1/9*(x+ln(3)+1)^3)-240*ln(3)*(1/2

*ln(x+ln(3)+1)*(x+ln(3)+1)^2-1/4*(x+ln(3)+1)^2)+288*ln(3)*(ln(x+ln(3)+1)*(x+ln(3)+1)-x-ln(3)-1)-60*ln(3)^2*(ln

(x+ln(3)+1)^4*(x+ln(3)+1)-4*ln(x+ln(3)+1)^3*(x+ln(3)+1)+12*ln(x+ln(3)+1)^2*(x+ln(3)+1)-24*ln(x+ln(3)+1)*(x+ln(

3)+1)+24*x+24*ln(3)+24)+60*ln(3)^2*(1/4*ln(x+ln(3)+1)^3*(x+ln(3)+1)^4-3/16*ln(x+ln(3)+1)^2*(x+ln(3)+1)^4+3/32*

ln(x+ln(3)+1)*(x+ln(3)+1)^4-3/128*(x+ln(3)+1)^4)+120*ln(3)*(1/4*ln(x+ln(3)+1)^4*(x+ln(3)+1)^4-1/4*ln(x+ln(3)+1

)^3*(x+ln(3)+1)^4+3/16*ln(x+ln(3)+1)^2*(x+ln(3)+1)^4-3/32*ln(x+ln(3)+1)*(x+ln(3)+1)^4+3/128*(x+ln(3)+1)^4)+120

*ln(3)^3*(1/2*ln(x+ln(3)+1)^4*(x+ln(3)+1)^2-ln(x+ln(3)+1)^3*(x+ln(3)+1)^2+3/2*ln(x+ln(3)+1)^2*(x+ln(3)+1)^2-3/

2*ln(x+ln(3)+1)*(x+ln(3)+1)^2+3/4*(x+ln(3)+1)^2)-180*ln(3)^2*(1/3*ln(x+ln(3)+1)^4*(x+ln(3)+1)^3-4/9*ln(x+ln(3)

+1)^3*(x+ln(3)+1)^3+4/9*ln(x+ln(3)+1)^2*(x+ln(3)+1)^3-8/27*ln(x+ln(3)+1)*(x+ln(3)+1)^3+8/81*(x+ln(3)+1)^3)+15*

ln(x+ln(3)+1)^4*ln(3)^2+6*ln(x+ln(3)+1)^4*ln(3)-120*ln(3)*(ln(x+ln(3)+1)^3*(x+ln(3)+1)-3*ln(x+ln(3)+1)^2*(x+ln

(3)+1)+6*ln(x+ln(3)+1)*(x+ln(3)+1)-6*x-6*ln(3)-6)-6*ln(x+ln(3)+1)^4*(x+ln(3)+1)-60*ln(3)^3*(ln(x+ln(3)+1)^4*(x

+ln(3)+1)-4*ln(x+ln(3)+1)^3*(x+ln(3)+1)+12*ln(x+ln(3)+1)^2*(x+ln(3)+1)-24*ln(x+ln(3)+1)*(x+ln(3)+1)+24*x+24*ln

(3)+24)-24*ln(3)^5*(ln(x+ln(3)+1)^3*(x+ln(3)+1)-3*ln(x+ln(3)+1)^2*(x+ln(3)+1)+6*ln(x+ln(3)+1)*(x+ln(3)+1)-6*x-

6*ln(3)-6)-240*ln(3)^2*(1/3*ln(x+ln(3)+1)^3*(x+ln(3)+1)^3-1/3*ln(x+ln(3)+1)^2*(x+ln(3)+1)^3+2/9*ln(x+ln(3)+1)*

(x+ln(3)+1)^3-2/27*(x+ln(3)+1)^3)-20*ln(x+ln(3)+1)^4*(x+ln(3)+1)^3-60*ln(3)^3*(1/3*ln(x+ln(3)+1)^4*(x+ln(3)+1)

^3-4/9*ln(x+ln(3)+1)^3*(x+ln(3)+1)^3+4/9*ln(x+ln(3)+1)^2*(x+ln(3)+1)^3-8/27*ln(x+ln(3)+1)*(x+ln(3)+1)^3+8/81*(

x+ln(3)+1)^3)+30*ln(3)^4*(1/2*ln(x+ln(3)+1)^4*(x+ln(3)+1)^2-ln(x+ln(3)+1)^3*(x+ln(3)+1)^2+3/2*ln(x+ln(3)+1)^2*

(x+ln(3)+1)^2-3/2*ln(x+ln(3)+1)*(x+ln(3)+1)^2+3/4*(x+ln(3)+1)^2)+ln(x+ln(3)+1)^4*(x+ln(3)+1)^6-6*ln(x+ln(3)+1)

^4*(x+ln(3)+1)^5+15*ln(x+ln(3)+1)^4*(x+ln(3)+1)^4+64*ln(3)^3*(ln(x+ln(3)+1)*(x+ln(3)+1)-x-ln(3)-1)+60*ln(3)^2*

(1/4*ln(x+ln(3)+1)^4*(x+ln(3)+1)^4-1/4*ln(x+ln(3)+1)^3*(x+ln(3)+1)^4+3/16*ln(x+ln(3)+1)^2*(x+ln(3)+1)^4-3/32*l

n(x+ln(3)+1)*(x+ln(3)+1)^4+3/128*(x+ln(3)+1)^4)-120*ln(3)^4*(ln(x+ln(3)+1)^3*(x+ln(3)+1)-3*ln(x+ln(3)+1)^2*(x+

ln(3)+1)+6*ln(x+ln(3)+1)*(x+ln(3)+1)-6*x-6*ln(3)-6)-8*ln(3)^4*ln(x+ln(3)+1)^2+120*ln(3)^2*(ln(x+ln(3)+1)^2*(x+

ln(3)+1)-2*ln(x+ln(3)+1)*(x+ln(3)+1)+2*x+2*ln(3)+2)-24*ln(3)*(1/5*ln(x+ln(3)+1)^3*(x+ln(3)+1)^5-3/25*(x+ln(3)+

1)^5*ln(x+ln(3)+1)^2+6/125*(x+ln(3)+1)^5*ln(x+ln(3)+1)-6/625*(x+ln(3)+1)^5)+180*ln(3)^2*(1/2*ln(x+ln(3)+1)^4*(

x+ln(3)+1)^2-ln(x+ln(3)+1)^3*(x+ln(3)+1)^2+3/2*ln(x+ln(3)+1)^2*(x+ln(3)+1)^2-3/2*ln(x+ln(3)+1)*(x+ln(3)+1)^2+3

/4*(x+ln(3)+1)^2)-72*ln(x+ln(3)+1)^2*ln(3)^2+ln(3)^6*ln(x+ln(3)+1)^4+40*ln(x+ln(3)+1)^2*(x+ln(3)+1)^3-240*ln(3

)*(1/3*ln(x+ln(3)+1)^3*(x+ln(3)+1)^3-1/3*ln(x+ln(3)+1)^2*(x+ln(3)+1)^3+2/9*ln(x+ln(3)+1)*(x+ln(3)+1)^3-2/27*(x

+ln(3)+1)^3)-72*ln(x+ln(3)+1)^2*(x+ln(3)+1)^2+240*ln(3)*(1/2*ln(x+ln(3)+1)^3*(x+ln(3)+1)^2-3/4*ln(x+ln(3)+1)^2

*(x+ln(3)+1)^2+3/4*ln(x+ln(3)+1)*(x+ln(3)+1)^2-3/8*(x+ln(3)+1)^2)-96*ln(3)^2*(1/2*ln(x+ln(3)+1)^2*(x+ln(3)+1)^

2-1/2*ln(x+ln(3)+1)*(x+ln(3)+1)^2+1/4*(x+ln(3)+1)^2)-80*ln(3)^3*(1/3*ln(x+ln(3)+1)^3*(x+ln(3)+1)^3-1/3*ln(x+ln

(3)+1)^2*(x+ln(3)+1)^3+2/9*ln(x+ln(3)+1)*(x+ln(3)+1)^3-2/27*(x+ln(3)+1)^3)-8*ln(x+ln(3)+1)^2*(x+ln(3)+1)^4+120

*ln(3)*(1/4*ln(x+ln(3)+1)^3*(x+ln(3)+1)^4-3/16*ln(x+ln(3)+1)^2*(x+ln(3)+1)^4+3/32*ln(x+ln(3)+1)*(x+ln(3)+1)^4-

3/128*(x+ln(3)+1)^4)+15*ln(x+ln(3)+1)^4*(x+ln(3)+1)^2+120*ln(3)*(1/2*ln(x+ln(3)+1)^4*(x+ln(3)+1)^2-ln(x+ln(3)+

1)^3*(x+ln(3)+1)^2+3/2*ln(x+ln(3)+1)^2*(x+ln(3)+1)^2-3/2*ln(x+ln(3)+1)*(x+ln(3)+1)^2+3/4*(x+ln(3)+1)^2)+56*ln(

x+ln(3)+1)^2*(x+ln(3)+1)+32*ln(3)^3*(ln(x+ln(3)+1)^2*(x+ln(3)+1)-2*ln(x+ln(3)+1)*(x+ln(3)+1)+2*x+2*ln(3)+2)-40

*ln(x+ln(3)+1)^2*ln(3)^3-240*ln(3)^2*(ln(x+ln(3)+1)^3*(x+ln(3)+1)-3*ln(x+ln(3)+1)^2*(x+ln(3)+1)+6*ln(x+ln(3)+1

)*(x+ln(3)+1)-6*x-6*ln(3)-6)-56*ln(x+ln(3)+1)^2*ln(3)+240*ln(3)^3*(1/2*ln(x+ln(3)+1)^3*(x+ln(3)+1)^2-3/4*ln(x+

ln(3)+1)^2*(x+ln(3)+1)^2+3/4*ln(x+ln(3)+1)*(x+ln(3)+1)^2-3/8*(x+ln(3)+1)^2)+240*ln(3)^2*(ln(x+ln(3)+1)*(x+ln(3

)+1)-x-ln(3)-1)-30*ln(3)^4*(ln(x+ln(3)+1)^4*(x+ln(3)+1)-4*ln(x+ln(3)+1)^3*(x+ln(3)+1)+12*ln(x+ln(3)+1)^2*(x+ln

(3)+1)-24*ln(x+ln(3)+1)*(x+ln(3)+1)+24*x+24*ln(3)+24)-6*ln(3)^5*(ln(x+ln(3)+1)^4*(x+ln(3)+1)-4*ln(x+ln(3)+1)^3

*(x+ln(3)+1)+12*ln(x+ln(3)+1)^2*(x+ln(3)+1)-24*ln(x+ln(3)+1)*(x+ln(3)+1)+24*x+24*ln(3)+24)+60*ln(3)^4*(1/2*ln(

x+ln(3)+1)^3*(x+ln(3)+1)^2-3/4*ln(x+ln(3)+1)^2*(x+ln(3)+1)^2+3/4*ln(x+ln(3)+1)*(x+ln(3)+1)^2-3/8*(x+ln(3)+1)^2

)+20*ln(x+ln(3)+1)^4*ln(3)^3+6*ln(x+ln(3)+1)^4*ln(3)^5+15*ln(x+ln(3)+1)^4*ln(3)^4+144*ln(3)*(ln(x+ln(3)+1)^2*(

x+ln(3)+1)-2*ln(x+ln(3)+1)*(x+ln(3)+1)+2*x+2*ln(3)+2)+96*ln(3)*(1/3*ln(x+ln(3)+1)^2*(x+ln(3)+1)^3-2/9*ln(x+ln(

3)+1)*(x+ln(3)+1)^3+2/27*(x+ln(3)+1)^3)+360*ln(3)^2*(1/2*ln(x+ln(3)+1)^3*(x+ln(3)+1)^2-3/4*ln(x+ln(3)+1)^2*(x+

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 3532 vs. \(2 (27) = 54\).
time = 0.51, size = 3532, normalized size = 126.14 \begin {gather*} \text {Too large to display} \end {gather*}

integrate(((6*x^5*log(3)+6*x^6+6*x^5)*log(x+log(3)+1)^4+4*x^6*log(x+log(3)+1)^3+((-32*x^3+24*x^2)*log(3)-32*x^

4-8*x^3+24*x^2)*log(x+log(3)+1)^2+(-16*x^4+16*x^3)*log(x+log(3)+1)+(32*x-32)*log(3)+32*x^2-32)/(x+log(3)+1),x,

1/54*(54*log(x + log(3) + 1)^4 - 36*log(x + log(3) + 1)^3 + 18*log(x + log(3) + 1)^2 - 6*log(x + log(3) + 1) +

1)*(x + log(3) + 1)^6 + 1/54*(36*log(x + log(3) + 1)^3 - 18*log(x + log(3) + 1)^2 + 6*log(x + log(3) + 1) - 1

)*(x + log(3) + 1)^6 - 36/3125*(625*(log(3) + 1)*log(x + log(3) + 1)^4 - 500*(log(3) + 1)*log(x + log(3) + 1)^

3 + 300*(log(3) + 1)*log(x + log(3) + 1)^2 - 120*(log(3) + 1)*log(x + log(3) + 1) + 24*log(3) + 24)*(x + log(3

) + 1)^5 - 24/625*(125*(log(3) + 1)*log(x + log(3) + 1)^3 - 75*(log(3) + 1)*log(x + log(3) + 1)^2 + 30*(log(3)

+ 1)*log(x + log(3) + 1) - 6*log(3) - 6)*(x + log(3) + 1)^5 + 6/3125*(625*log(x + log(3) + 1)^4 - 500*log(x +

log(3) + 1)^3 + 300*log(x + log(3) + 1)^2 - 120*log(x + log(3) + 1) + 24)*(x + log(3) + 1)^5 + 6/5*(log(3)^6

+ 6*log(3)^5 + 15*log(3)^4 + 20*log(3)^3 + 15*log(3)^2 + 6*log(3) + 1)*log(x + log(3) + 1)^5 - 6/5*(log(3)^5 +

5*log(3)^4 + 10*log(3)^3 + 10*log(3)^2 + 5*log(3) + 1)*log(x + log(3) + 1)^5 + 45/64*(32*(log(3)^2 + 2*log(3)

+ 1)*log(x + log(3) + 1)^4 - 32*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1)^3 + 24*(log(3)^2 + 2*log(3) + 1

)*log(x + log(3) + 1)^2 + 3*log(3)^2 - 12*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1) + 6*log(3) + 3)*(x + l

og(3) + 1)^4 - 15/64*(32*(log(3) + 1)*log(x + log(3) + 1)^4 - 32*(log(3) + 1)*log(x + log(3) + 1)^3 + 24*(log(

3) + 1)*log(x + log(3) + 1)^2 - 12*(log(3) + 1)*log(x + log(3) + 1) + 3*log(3) + 3)*(x + log(3) + 1)^4 + 15/32

*(32*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1)^3 - 24*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1)^2 - 3*

log(3)^2 + 12*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1) - 6*log(3) - 3)*(x + log(3) + 1)^4 - (8*log(x + lo

g(3) + 1)^2 - 4*log(x + log(3) + 1) + 1)*(x + log(3) + 1)^4 + (log(3)^6 + 6*log(3)^5 + 15*log(3)^4 + 20*log(3)

^3 + 15*log(3)^2 + 6*log(3) + 1)*log(x + log(3) + 1)^4 - 40/27*(27*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)*log(

x + log(3) + 1)^4 - 36*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1)^3 + 8*log(3)^3 + 36*(log(3)^

3 + 3*log(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1)^2 + 24*log(3)^2 - 24*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)

*log(x + log(3) + 1) + 24*log(3) + 8)*(x + log(3) + 1)^3 + 20/27*(27*(log(3)^2 + 2*log(3) + 1)*log(x + log(3)

+ 1)^4 - 36*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1)^3 + 36*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1)

^2 + 8*log(3)^2 - 24*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1) + 16*log(3) + 8)*(x + log(3) + 1)^3 - 80/27

*(9*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1)^3 - 2*log(3)^3 - 9*(log(3)^3 + 3*log(3)^2 + 3*l

og(3) + 1)*log(x + log(3) + 1)^2 - 6*log(3)^2 + 6*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1) -

6*log(3) - 2)*(x + log(3) + 1)^3 + 128/27*(9*(log(3) + 1)*log(x + log(3) + 1)^2 - 6*(log(3) + 1)*log(x + log(

3) + 1) + 2*log(3) + 2)*(x + log(3) + 1)^3 - 8/27*(9*log(x + log(3) + 1)^2 - 6*log(x + log(3) + 1) + 2)*(x + l

og(3) + 1)^3 + x^4 - 28/9*x^3*(log(3) + 1) - 32/3*(log(3)^4 + 4*log(3)^3 + 6*log(3)^2 + 4*log(3) + 1)*log(x +

log(3) + 1)^3 + 8/3*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1)^3 + 8*(log(3)^2 + 2*log(3) + 1)

*log(x + log(3) + 1)^3 + 45/2*(2*(log(3)^4 + 4*log(3)^3 + 6*log(3)^2 + 4*log(3) + 1)*log(x + log(3) + 1)^4 + 3

*log(3)^4 - 4*(log(3)^4 + 4*log(3)^3 + 6*log(3)^2 + 4*log(3) + 1)*log(x + log(3) + 1)^3 + 12*log(3)^3 + 6*(log

(3)^4 + 4*log(3)^3 + 6*log(3)^2 + 4*log(3) + 1)*log(x + log(3) + 1)^2 + 18*log(3)^2 - 6*(log(3)^4 + 4*log(3)^3

+ 6*log(3)^2 + 4*log(3) + 1)*log(x + log(3) + 1) + 12*log(3) + 3)*(x + log(3) + 1)^2 - 15*(2*(log(3)^3 + 3*lo

g(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1)^4 - 4*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1)^3

+ 3*log(3)^3 + 6*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1)^2 + 9*log(3)^2 - 6*(log(3)^3 + 3*l

og(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1) + 9*log(3) + 3)*(x + log(3) + 1)^2 - 15/2*(3*log(3)^4 - 4*(log(3)^

4 + 4*log(3)^3 + 6*log(3)^2 + 4*log(3) + 1)*log(x + log(3) + 1)^3 + 12*log(3)^3 + 6*(log(3)^4 + 4*log(3)^3 + 6

*log(3)^2 + 4*log(3) + 1)*log(x + log(3) + 1)^2 + 18*log(3)^2 - 6*(log(3)^4 + 4*log(3)^3 + 6*log(3)^2 + 4*log(

3) + 1)*log(x + log(3) + 1) + 12*log(3) + 3)*(x + log(3) + 1)^2 - 48*(2*(log(3)^2 + 2*log(3) + 1)*log(x + log(

3) + 1)^2 + log(3)^2 - 2*(log(3)^2 + 2*log(3) + 1)*log(x + log(3) + 1) + 2*log(3) + 1)*(x + log(3) + 1)^2 + 6*

(2*(log(3) + 1)*log(x + log(3) + 1)^2 - 2*(log(3) + 1)*log(x + log(3) + 1) + log(3) + 1)*(x + log(3) + 1)^2 +

6*(2*log(x + log(3) + 1)^2 - 2*log(x + log(3) + 1) + 1)*(x + log(3) + 1)^2 + 26/3*(log(3)^2 + 2*log(3) + 1)*x^

2 - 16/9*x^3 + 20/3*x^2*(log(3) + 1) + 8*(log(3)^4 + 4*log(3)^3 + 6*log(3)^2 + 4*log(3) + 1)*log(x + log(3) +

1)^2 + 8*(log(3)^3 + 3*log(3)^2 + 3*log(3) + 1)*log(x + log(3) + 1)^2 - 36*(24*log(3)^5 + (log(3)^5 + 5*log(3)

^4 + 10*log(3)^3 + 10*log(3)^2 + 5*log(3) + 1)*log(x + log(3) + 1)^4 + 120*log(3)^4 - 4*(log(3)^5 + 5*log(3)^4

+ 10*log(3)^3 + 10*log(3)^2 + 5*log(3) + 1)*log(x + log(3) + 1)^3 + 240*log(3)^3 + 12*(log(3)^5 + 5*log(3)^4

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Fricas [A]
time = 0.38, size = 40, normalized size = 1.43 \begin {gather*} x^{6} \log \left (x + \log \left (3\right ) + 1\right )^{4} - 8 \, {\left (x^{4} - x^{3}\right )} \log \left (x + \log \left (3\right ) + 1\right )^{2} + 16 \, x^{2} - 32 \, x \end {gather*}

integrate(((6*x^5*log(3)+6*x^6+6*x^5)*log(x+log(3)+1)^4+4*x^6*log(x+log(3)+1)^3+((-32*x^3+24*x^2)*log(3)-32*x^

4-8*x^3+24*x^2)*log(x+log(3)+1)^2+(-16*x^4+16*x^3)*log(x+log(3)+1)+(32*x-32)*log(3)+32*x^2-32)/(x+log(3)+1),x,

x^6*log(x + log(3) + 1)^4 - 8*(x^4 - x^3)*log(x + log(3) + 1)^2 + 16*x^2 - 32*x

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Sympy [A]
time = 0.10, size = 41, normalized size = 1.46 \begin {gather*} x^{6} \log {\left (x + 1 + \log {\left (3 \right )} \right )}^{4} + 16 x^{2} - 32 x + \left (- 8 x^{4} + 8 x^{3}\right ) \log {\left (x + 1 + \log {\left (3 \right )} \right )}^{2} \end {gather*}

integrate(((6*x**5*ln(3)+6*x**6+6*x**5)*ln(x+ln(3)+1)**4+4*x**6*ln(x+ln(3)+1)**3+((-32*x**3+24*x**2)*ln(3)-32*

x**4-8*x**3+24*x**2)*ln(x+ln(3)+1)**2+(-16*x**4+16*x**3)*ln(x+ln(3)+1)+(32*x-32)*ln(3)+32*x**2-32)/(x+ln(3)+1)

x**6*log(x + 1 + log(3))**4 + 16*x**2 - 32*x + (-8*x**4 + 8*x**3)*log(x + 1 + log(3))**2

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Giac [A]
time = 0.45, size = 40, normalized size = 1.43 \begin {gather*} x^{6} \log \left (x + \log \left (3\right ) + 1\right )^{4} - 8 \, {\left (x^{4} - x^{3}\right )} \log \left (x + \log \left (3\right ) + 1\right )^{2} + 16 \, x^{2} - 32 \, x \end {gather*}

integrate(((6*x^5*log(3)+6*x^6+6*x^5)*log(x+log(3)+1)^4+4*x^6*log(x+log(3)+1)^3+((-32*x^3+24*x^2)*log(3)-32*x^

4-8*x^3+24*x^2)*log(x+log(3)+1)^2+(-16*x^4+16*x^3)*log(x+log(3)+1)+(32*x-32)*log(3)+32*x^2-32)/(x+log(3)+1),x,

x^6*log(x + log(3) + 1)^4 - 8*(x^4 - x^3)*log(x + log(3) + 1)^2 + 16*x^2 - 32*x

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Mupad [F(-1)]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \text {Hanged} \end {gather*}

int((log(3)*(32*x - 32) + log(x + log(3) + 1)^2*(log(3)*(24*x^2 - 32*x^3) + 24*x^2 - 8*x^3 - 32*x^4) + 4*x^6*l

og(x + log(3) + 1)^3 + 32*x^2 + log(x + log(3) + 1)*(16*x^3 - 16*x^4) + log(x + log(3) + 1)^4*(6*x^5*log(3) +

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3.93.18 \(\int \frac {-32+32 x^2+(-32+32 x) \log (3)+(16 x^3-16 x^4) \log (1+x+\log (3))+(24 x^2-8 x^3-32 x^4+(24 x^2-32 x^3) \log (3)) \log ^2(1+x+\log (3))+4 x^6 \log ^3(1+x+\log (3))+(6 x^5+6 x^6+6 x^5 \log (3)) \log ^4(1+x+\log (3))}{1+x+\log (3)} \, dx\) [9218]