3.23.4 \(\int \frac {1500+800 x-480 x^2-384 x^3-64 x^4+(3000+3600 x+1440 x^2+192 x^3) \log ^2(3)+(900+120 x-336 x^2-96 x^3+(1800+1440 x+288 x^2) \log ^2(3)) \log (-2+x-3 \log ^2(3))+(180-48 x-48 x^2+(360+144 x) \log ^2(3)) \log ^2(-2+x-3 \log ^2(3))+(12-8 x+24 \log ^2(3)) \log ^3(-2+x-3 \log ^2(3))}{2-x+3 \log ^2(3)} \, dx\)

Optimal. Leaf size=19 \[ -1+\left (5+2 x+\log \left (-2+x-3 \log ^2(3)\right )\right )^4 \]

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Rubi [A]  time = 0.23, antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 3, integrand size = 152, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6688, 12, 6686} \begin {gather*} \left (2 x+\log \left (x-2-3 \log ^2(3)\right )+5\right )^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(1500 + 800*x - 480*x^2 - 384*x^3 - 64*x^4 + (3000 + 3600*x + 1440*x^2 + 192*x^3)*Log[3]^2 + (900 + 120*x
- 336*x^2 - 96*x^3 + (1800 + 1440*x + 288*x^2)*Log[3]^2)*Log[-2 + x - 3*Log[3]^2] + (180 - 48*x - 48*x^2 + (36
0 + 144*x)*Log[3]^2)*Log[-2 + x - 3*Log[3]^2]^2 + (12 - 8*x + 24*Log[3]^2)*Log[-2 + x - 3*Log[3]^2]^3)/(2 - x
+ 3*Log[3]^2),x]

[Out]

(5 + 2*x + Log[-2 + x - 3*Log[3]^2])^4

Rule 12

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

Rule 6686

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

Rule 6688

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (3-2 x+6 \log ^2(3)\right ) \left (5+2 x+\log \left (-2+x-3 \log ^2(3)\right )\right )^3}{2-x+3 \log ^2(3)} \, dx\\ &=4 \int \frac {\left (3-2 x+6 \log ^2(3)\right ) \left (5+2 x+\log \left (-2+x-3 \log ^2(3)\right )\right )^3}{2-x+3 \log ^2(3)} \, dx\\ &=\left (5+2 x+\log \left (-2+x-3 \log ^2(3)\right )\right )^4\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 17, normalized size = 0.89 \begin {gather*} \left (5+2 x+\log \left (-2+x-3 \log ^2(3)\right )\right )^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1500 + 800*x - 480*x^2 - 384*x^3 - 64*x^4 + (3000 + 3600*x + 1440*x^2 + 192*x^3)*Log[3]^2 + (900 +
120*x - 336*x^2 - 96*x^3 + (1800 + 1440*x + 288*x^2)*Log[3]^2)*Log[-2 + x - 3*Log[3]^2] + (180 - 48*x - 48*x^2
+ (360 + 144*x)*Log[3]^2)*Log[-2 + x - 3*Log[3]^2]^2 + (12 - 8*x + 24*Log[3]^2)*Log[-2 + x - 3*Log[3]^2]^3)/(
2 - x + 3*Log[3]^2),x]

[Out]

(5 + 2*x + Log[-2 + x - 3*Log[3]^2])^4

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fricas [B]  time = 0.65, size = 101, normalized size = 5.32 \begin {gather*} 16 \, x^{4} + 4 \, {\left (2 \, x + 5\right )} \log \left (-3 \, \log \relax (3)^{2} + x - 2\right )^{3} + \log \left (-3 \, \log \relax (3)^{2} + x - 2\right )^{4} + 160 \, x^{3} + 6 \, {\left (4 \, x^{2} + 20 \, x + 25\right )} \log \left (-3 \, \log \relax (3)^{2} + x - 2\right )^{2} + 600 \, x^{2} + 4 \, {\left (8 \, x^{3} + 60 \, x^{2} + 150 \, x + 125\right )} \log \left (-3 \, \log \relax (3)^{2} + x - 2\right ) + 1000 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*log(3)^2-8*x+12)*log(-3*log(3)^2+x-2)^3+((144*x+360)*log(3)^2-48*x^2-48*x+180)*log(-3*log(3)^2+
x-2)^2+((288*x^2+1440*x+1800)*log(3)^2-96*x^3-336*x^2+120*x+900)*log(-3*log(3)^2+x-2)+(192*x^3+1440*x^2+3600*x
+3000)*log(3)^2-64*x^4-384*x^3-480*x^2+800*x+1500)/(3*log(3)^2+2-x),x, algorithm="fricas")

[Out]

16*x^4 + 4*(2*x + 5)*log(-3*log(3)^2 + x - 2)^3 + log(-3*log(3)^2 + x - 2)^4 + 160*x^3 + 6*(4*x^2 + 20*x + 25)
*log(-3*log(3)^2 + x - 2)^2 + 600*x^2 + 4*(8*x^3 + 60*x^2 + 150*x + 125)*log(-3*log(3)^2 + x - 2) + 1000*x

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giac [B]  time = 1.30, size = 112, normalized size = 5.89 \begin {gather*} 16 \, x^{4} + 4 \, {\left (2 \, x + 5\right )} \log \left (-3 \, \log \relax (3)^{2} + x - 2\right )^{3} + \log \left (-3 \, \log \relax (3)^{2} + x - 2\right )^{4} + 160 \, x^{3} + 6 \, {\left (4 \, x^{2} + 20 \, x + 25\right )} \log \left (-3 \, \log \relax (3)^{2} + x - 2\right )^{2} + 600 \, x^{2} + 8 \, {\left (4 \, x^{3} + 30 \, x^{2} + 75 \, x\right )} \log \left (-3 \, \log \relax (3)^{2} + x - 2\right ) + 1000 \, x + 500 \, \log \left (-3 \, \log \relax (3)^{2} + x - 2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*log(3)^2-8*x+12)*log(-3*log(3)^2+x-2)^3+((144*x+360)*log(3)^2-48*x^2-48*x+180)*log(-3*log(3)^2+
x-2)^2+((288*x^2+1440*x+1800)*log(3)^2-96*x^3-336*x^2+120*x+900)*log(-3*log(3)^2+x-2)+(192*x^3+1440*x^2+3600*x
+3000)*log(3)^2-64*x^4-384*x^3-480*x^2+800*x+1500)/(3*log(3)^2+2-x),x, algorithm="giac")

[Out]

16*x^4 + 4*(2*x + 5)*log(-3*log(3)^2 + x - 2)^3 + log(-3*log(3)^2 + x - 2)^4 + 160*x^3 + 6*(4*x^2 + 20*x + 25)
*log(-3*log(3)^2 + x - 2)^2 + 600*x^2 + 8*(4*x^3 + 30*x^2 + 75*x)*log(-3*log(3)^2 + x - 2) + 1000*x + 500*log(
-3*log(3)^2 + x - 2)

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maple [B]  time = 0.42, size = 110, normalized size = 5.79

method	result	size
risch	\(\ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{4}+\left (8 x +20\right ) \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+\left (24 x^{2}+120 x +150\right ) \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+\left (32 x^{3}+240 x^{2}+600 x \right ) \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+16 x^{4}+160 x^{3}+600 x^{2}+1000 x +500 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )\)	\(110\)
norman	\(\ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{4}+500 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+1000 x +600 x^{2}+160 x^{3}+16 x^{4}+150 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+20 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+600 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) x +240 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) x^{2}+32 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) x^{3}+120 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2} x +24 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2} x^{2}+8 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3} x\)	\(162\)
derivativedivides	\(-11664+5832 x -17496 \ln \relax (3)^{2}+2916 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+1728 \ln \relax (3)^{6} \left (-3 \ln \relax (3)^{2}+x -2\right )+864 \ln \relax (3)^{4} \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+3888 \ln \relax (3)^{4} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+8640 \ln \relax (3)^{4} \left (-3 \ln \relax (3)^{2}+x -2\right )+192 \ln \relax (3)^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+648 \ln \relax (3)^{2} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+2736 \ln \relax (3)^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+8 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3} \left (-3 \ln \relax (3)^{2}+x -2\right )+24 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+32 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+14256 \ln \relax (3)^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )+216 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )+432 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+1944 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )+216 \ln \relax (3)^{4} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+24 \ln \relax (3)^{2} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+864 \ln \relax (3)^{6} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+144 \ln \relax (3)^{2} \left (\ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )-2 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )-6 \ln \relax (3)^{2}+2 x -4\right )+2880 \ln \relax (3)^{2} \left (\ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )+3 \ln \relax (3)^{2}-x +2\right )+576 \ln \relax (3)^{2} \left (\frac {\ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}}{2}-\frac {\left (-3 \ln \relax (3)^{2}+x -2\right )^{2}}{4}\right )+864 \ln \relax (3)^{4} \left (\ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )+3 \ln \relax (3)^{2}-x +2\right )+5832 \ln \relax (3)^{2} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+1944 \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+\ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{4}+16 \left (-3 \ln \relax (3)^{2}+x -2\right )^{4}+288 \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+36 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+486 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}\)	\(616\)
default	\(-11664+5832 x -17496 \ln \relax (3)^{2}+2916 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+1728 \ln \relax (3)^{6} \left (-3 \ln \relax (3)^{2}+x -2\right )+864 \ln \relax (3)^{4} \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+3888 \ln \relax (3)^{4} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+8640 \ln \relax (3)^{4} \left (-3 \ln \relax (3)^{2}+x -2\right )+192 \ln \relax (3)^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+648 \ln \relax (3)^{2} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+2736 \ln \relax (3)^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+8 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3} \left (-3 \ln \relax (3)^{2}+x -2\right )+24 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+32 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+14256 \ln \relax (3)^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )+216 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )+432 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+1944 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )+216 \ln \relax (3)^{4} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+24 \ln \relax (3)^{2} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+864 \ln \relax (3)^{6} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+144 \ln \relax (3)^{2} \left (\ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2} \left (-3 \ln \relax (3)^{2}+x -2\right )-2 \ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )-6 \ln \relax (3)^{2}+2 x -4\right )+2880 \ln \relax (3)^{2} \left (\ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )+3 \ln \relax (3)^{2}-x +2\right )+576 \ln \relax (3)^{2} \left (\frac {\ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}}{2}-\frac {\left (-3 \ln \relax (3)^{2}+x -2\right )^{2}}{4}\right )+864 \ln \relax (3)^{4} \left (\ln \left (-3 \ln \relax (3)^{2}+x -2\right ) \left (-3 \ln \relax (3)^{2}+x -2\right )+3 \ln \relax (3)^{2}-x +2\right )+5832 \ln \relax (3)^{2} \ln \left (-3 \ln \relax (3)^{2}+x -2\right )+1944 \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}+\ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{4}+16 \left (-3 \ln \relax (3)^{2}+x -2\right )^{4}+288 \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+36 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{3}+486 \ln \left (-3 \ln \relax (3)^{2}+x -2\right )^{2}\)	\(616\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((24*ln(3)^2-8*x+12)*ln(-3*ln(3)^2+x-2)^3+((144*x+360)*ln(3)^2-48*x^2-48*x+180)*ln(-3*ln(3)^2+x-2)^2+((288
*x^2+1440*x+1800)*ln(3)^2-96*x^3-336*x^2+120*x+900)*ln(-3*ln(3)^2+x-2)+(192*x^3+1440*x^2+3600*x+3000)*ln(3)^2-
64*x^4-384*x^3-480*x^2+800*x+1500)/(3*ln(3)^2+2-x),x,method=_RETURNVERBOSE)

[Out]

ln(-3*ln(3)^2+x-2)^4+(8*x+20)*ln(-3*ln(3)^2+x-2)^3+(24*x^2+120*x+150)*ln(-3*ln(3)^2+x-2)^2+(32*x^3+240*x^2+600
*x)*ln(-3*ln(3)^2+x-2)+16*x^4+160*x^3+600*x^2+1000*x+500*ln(-3*ln(3)^2+x-2)

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maxima [B]  time = 0.53, size = 1368, normalized size = 72.00 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*log(3)^2-8*x+12)*log(-3*log(3)^2+x-2)^3+((144*x+360)*log(3)^2-48*x^2-48*x+180)*log(-3*log(3)^2+
x-2)^2+((288*x^2+1440*x+1800)*log(3)^2-96*x^3-336*x^2+120*x+900)*log(-3*log(3)^2+x-2)+(192*x^3+1440*x^2+3600*x
+3000)*log(3)^2-64*x^4-384*x^3-480*x^2+800*x+1500)/(3*log(3)^2+2-x),x, algorithm="maxima")

[Out]

-6*log(3)^2*log(-3*log(3)^2 + x - 2)^4 - 120*log(3)^2*log(-3*log(3)^2 + x - 2)^3 + 2*(3*log(3)^2 + 2)*log(-3*l
og(3)^2 + x - 2)^4 + 64/3*(3*log(3)^2 + 2)*x^3 + 16*x^4 - 144*(2*(3*log(3)^2 + 2)*x + x^2 + 2*(9*log(3)^4 + 12
*log(3)^2 + 4)*log(-3*log(3)^2 + x - 2))*log(3)^2*log(-3*log(3)^2 + x - 2) - 1440*((3*log(3)^2 + 2)*log(-3*log
(3)^2 + x - 2) + x)*log(3)^2*log(-3*log(3)^2 + x - 2) - 1800*log(3)^2*log(3*log(3)^2 - x + 2)*log(-3*log(3)^2
+ x - 2) + 16*(9*log(3)^4 + 12*log(3)^2 + 4)*log(-3*log(3)^2 + x - 2)^3 + 16*(3*log(3)^2 + 2)*log(-3*log(3)^2
+ x - 2)^3 - 3*log(-3*log(3)^2 + x - 2)^4 + 12*(3*log(3)^2 - x + 2)^2*(2*log(-3*log(3)^2 + x - 2)^2 - 2*log(-3
*log(3)^2 + x - 2) + 1) + 32*(9*log(3)^4 + 12*log(3)^2 + 4)*x^2 + 152*(3*log(3)^2 + 2)*x^2 + 352/3*x^3 - 48*((
3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2)^3 - 3*(3*log(3)^2 - x + 2)*(log(-3*log(3)^2 + x - 2)^2 - 2*log(-3*log
(3)^2 + x - 2) + 2))*log(3)^2 - 32*(3*(3*log(3)^2 + 2)*x^2 + 2*x^3 + 6*(9*log(3)^4 + 12*log(3)^2 + 4)*x + 6*(2
7*log(3)^6 + 54*log(3)^4 + 36*log(3)^2 + 8)*log(-3*log(3)^2 + x - 2))*log(3)^2 + 72*(2*(9*log(3)^4 + 12*log(3)
^2 + 4)*log(-3*log(3)^2 + x - 2)^2 + 6*(3*log(3)^2 + 2)*x + x^2 + 6*(9*log(3)^4 + 12*log(3)^2 + 4)*log(-3*log(
3)^2 + x - 2))*log(3)^2 + 720*((3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2)^2 + 2*(3*log(3)^2 + 2)*log(-3*log(3)^
2 + x - 2) + 2*x)*log(3)^2 - 720*(2*(3*log(3)^2 + 2)*x + x^2 + 2*(9*log(3)^4 + 12*log(3)^2 + 4)*log(-3*log(3)^
2 + x - 2))*log(3)^2 - 3600*((3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2) + x)*log(3)^2 + 900*(2*log(3*log(3)^2 -
x + 2)*log(-3*log(3)^2 + x - 2) - log(-3*log(3)^2 + x - 2)^2)*log(3)^2 - 3000*log(3)^2*log(3*log(3)^2 - x + 2
) - 48*(27*log(3)^6 + 54*log(3)^4 + 36*log(3)^2 + 8)*log(-3*log(3)^2 + x - 2)^2 - 168*(9*log(3)^4 + 12*log(3)^
2 + 4)*log(-3*log(3)^2 + x - 2)^2 + 60*(3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2)^2 - 60*log(-3*log(3)^2 + x -
2)^3 - 96*((3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2)^2 + 6*log(3)^2 - 2*(3*log(3)^2 + 2)*log(-3*log(3)^2 + x -
2) + 4)*(3*log(3)^2 - x + 2) - 8*(log(-3*log(3)^2 + x - 2)^3 - 3*log(-3*log(3)^2 + x - 2)^2 + 6*log(-3*log(3)
^2 + x - 2) - 6)*(3*log(3)^2 - x + 2) - 48*(3*log(3)^2 - x + 2)*(log(-3*log(3)^2 + x - 2)^2 - 2*log(-3*log(3)^
2 + x - 2) + 2) + 64*(27*log(3)^6 + 54*log(3)^4 + 36*log(3)^2 + 8)*x + 208*(9*log(3)^4 + 12*log(3)^2 + 4)*x -
24*(3*log(3)^2 + 2)*x + 156*x^2 + 64*(81*log(3)^8 + 216*log(3)^6 + 216*log(3)^4 + 96*log(3)^2 + 16)*log(-3*log
(3)^2 + x - 2) + 208*(27*log(3)^6 + 54*log(3)^4 + 36*log(3)^2 + 8)*log(-3*log(3)^2 + x - 2) - 24*(9*log(3)^4 +
12*log(3)^2 + 4)*log(-3*log(3)^2 + x - 2) + 16*(3*(3*log(3)^2 + 2)*x^2 + 2*x^3 + 6*(9*log(3)^4 + 12*log(3)^2
+ 4)*x + 6*(27*log(3)^6 + 54*log(3)^4 + 36*log(3)^2 + 8)*log(-3*log(3)^2 + x - 2))*log(-3*log(3)^2 + x - 2) +
168*(2*(3*log(3)^2 + 2)*x + x^2 + 2*(9*log(3)^4 + 12*log(3)^2 + 4)*log(-3*log(3)^2 + x - 2))*log(-3*log(3)^2 +
x - 2) - 680*(3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2) - 120*((3*log(3)^2 + 2)*log(-3*log(3)^2 + x - 2) + x)*
log(-3*log(3)^2 + x - 2) - 450*log(-3*log(3)^2 + x - 2)^2 - 680*x - 1500*log(3*log(3)^2 - x + 2)

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mupad [B]  time = 1.66, size = 109, normalized size = 5.74 \begin {gather*} 1000\,x+500\,\ln \left (x-3\,{\ln \relax (3)}^2-2\right )+{\ln \left (x-3\,{\ln \relax (3)}^2-2\right )}^3\,\left (8\,x+20\right )+\ln \left (x-3\,{\ln \relax (3)}^2-2\right )\,\left (32\,x^3+240\,x^2+600\,x\right )+{\ln \left (x-3\,{\ln \relax (3)}^2-2\right )}^2\,\left (24\,x^2+120\,x+150\right )+{\ln \left (x-3\,{\ln \relax (3)}^2-2\right )}^4+600\,x^2+160\,x^3+16\,x^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((800*x + log(x - 3*log(3)^2 - 2)*(120*x + log(3)^2*(1440*x + 288*x^2 + 1800) - 336*x^2 - 96*x^3 + 900) + l
og(x - 3*log(3)^2 - 2)^3*(24*log(3)^2 - 8*x + 12) + log(3)^2*(3600*x + 1440*x^2 + 192*x^3 + 3000) - 480*x^2 -
384*x^3 - 64*x^4 - log(x - 3*log(3)^2 - 2)^2*(48*x - log(3)^2*(144*x + 360) + 48*x^2 - 180) + 1500)/(3*log(3)^
2 - x + 2),x)

[Out]

1000*x + 500*log(x - 3*log(3)^2 - 2) + log(x - 3*log(3)^2 - 2)^3*(8*x + 20) + log(x - 3*log(3)^2 - 2)*(600*x +
240*x^2 + 32*x^3) + log(x - 3*log(3)^2 - 2)^2*(120*x + 24*x^2 + 150) + log(x - 3*log(3)^2 - 2)^4 + 600*x^2 +
160*x^3 + 16*x^4

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sympy [B]  time = 0.41, size = 112, normalized size = 5.89 \begin {gather*} 16 x^{4} + 160 x^{3} + 600 x^{2} + 1000 x + \left (8 x + 20\right ) \log {\left (x - 3 \log {\relax (3 )}^{2} - 2 \right )}^{3} + \left (24 x^{2} + 120 x + 150\right ) \log {\left (x - 3 \log {\relax (3 )}^{2} - 2 \right )}^{2} + \left (32 x^{3} + 240 x^{2} + 600 x\right ) \log {\left (x - 3 \log {\relax (3 )}^{2} - 2 \right )} + \log {\left (x - 3 \log {\relax (3 )}^{2} - 2 \right )}^{4} + 500 \log {\left (x - 3 \log {\relax (3 )}^{2} - 2 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*ln(3)**2-8*x+12)*ln(-3*ln(3)**2+x-2)**3+((144*x+360)*ln(3)**2-48*x**2-48*x+180)*ln(-3*ln(3)**2+
x-2)**2+((288*x**2+1440*x+1800)*ln(3)**2-96*x**3-336*x**2+120*x+900)*ln(-3*ln(3)**2+x-2)+(192*x**3+1440*x**2+3
600*x+3000)*ln(3)**2-64*x**4-384*x**3-480*x**2+800*x+1500)/(3*ln(3)**2+2-x),x)

[Out]

16*x**4 + 160*x**3 + 600*x**2 + 1000*x + (8*x + 20)*log(x - 3*log(3)**2 - 2)**3 + (24*x**2 + 120*x + 150)*log(
x - 3*log(3)**2 - 2)**2 + (32*x**3 + 240*x**2 + 600*x)*log(x - 3*log(3)**2 - 2) + log(x - 3*log(3)**2 - 2)**4
+ 500*log(x - 3*log(3)**2 - 2)

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