3.13.23 \(\int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+(-20736+10336 x+576 x^2-288 x^3) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+(-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7) \log (2-x)+(-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5) \log ^2(2-x)+(-41472+6912 x+5760 x^2+576 x^3) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx\)
Optimal. Leaf size=24 \[ \frac {x}{\frac {19}{4}+\left (9 (6+x)^2+\log (2-x)\right )^2} \]
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Rubi [F] time = 9.64, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-3359384 + 1669324*x + 556416*x^2 - 155808*x^3 - 54432*x^4 - 3888*x^5 + (-20736 + 10336*x + 576*x^2 - 288
*x^3)*Log[2 - x] + (-32 + 16*x)*Log[2 - x]^2)/(-352670651858 - 293870933783*x - 39176763264*x^2 + 45714497472*
x^3 + 26665854480*x^4 + 6983855640*x^5 + 1058158080*x^6 + 95738112*x^7 + 4828896*x^8 + 104976*x^9 + (-43537616
64 - 2176749504*x + 362824416*x^2 + 503887536*x^3 + 151165440*x^4 + 21835008*x^5 + 1586304*x^6 + 46656*x^7)*Lo
g[2 - x] + (-20155696 - 3359080*x + 3359232*x^2 + 1306368*x^3 + 171072*x^4 + 7776*x^5)*Log[2 - x]^2 + (-41472
+ 6912*x + 5760*x^2 + 576*x^3)*Log[2 - x]^3 + (-32 + 16*x)*Log[2 - x]^4),x]
[Out]
-18432*Defer[Int][(419923 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 - x] + 864*x*Log[2 - x] + 7
2*x^2*Log[2 - x] + 4*Log[2 - x]^2)^(-2), x] - 36864*Defer[Int][1/((-2 + x)*(419923 + 279936*x + 69984*x^2 + 77
76*x^3 + 324*x^4 + 2592*Log[2 - x] + 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Log[2 - x]^2)^2), x] - 1123776*D
efer[Int][x/(419923 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 - x] + 864*x*Log[2 - x] + 72*x^2*
Log[2 - x] + 4*Log[2 - x]^2)^2, x] - 560160*Defer[Int][x^2/(419923 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4
+ 2592*Log[2 - x] + 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Log[2 - x]^2)^2, x] - 93312*Defer[Int][x^3/(4199
23 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 - x] + 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Lo
g[2 - x]^2)^2, x] - 5184*Defer[Int][x^4/(419923 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 - x]
+ 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Log[2 - x]^2)^2, x] - 32*Defer[Int][Log[2 - x]/(419923 + 279936*x +
69984*x^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 - x] + 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Log[2 - x]^2)^2,
x] - 64*Defer[Int][Log[2 - x]/((-2 + x)*(419923 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 - x]
+ 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Log[2 - x]^2)^2), x] - 3456*Defer[Int][(x*Log[2 - x])/(419923 + 279
936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 - x] + 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Log[2 - x]
^2)^2, x] - 576*Defer[Int][(x^2*Log[2 - x])/(419923 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 -
x] + 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Log[2 - x]^2)^2, x] + 4*Defer[Int][(419923 + 279936*x + 69984*x
^2 + 7776*x^3 + 324*x^4 + 2592*Log[2 - x] + 864*x*Log[2 - x] + 72*x^2*Log[2 - x] + 4*Log[2 - x]^2)^(-1), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (839846-417331 x-139104 x^2+38952 x^3+13608 x^4+972 x^5+8 \left (648-323 x-18 x^2+9 x^3\right ) \log (2-x)-4 (-2+x) \log ^2(2-x)\right )}{(2-x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+72 (6+x)^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx\\ &=4 \int \frac {839846-417331 x-139104 x^2+38952 x^3+13608 x^4+972 x^5+8 \left (648-323 x-18 x^2+9 x^3\right ) \log (2-x)-4 (-2+x) \log ^2(2-x)}{(2-x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+72 (6+x)^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx\\ &=4 \int \left (-\frac {8 x \left (-215+72 x+18 x^2\right ) \left (324+108 x+9 x^2+\log (2-x)\right )}{(-2+x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}+\frac {1}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)}\right ) \, dx\\ &=4 \int \frac {1}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)} \, dx-32 \int \frac {x \left (-215+72 x+18 x^2\right ) \left (324+108 x+9 x^2+\log (2-x)\right )}{(-2+x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx\\ &=4 \int \frac {1}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)} \, dx-32 \int \left (\frac {324+108 x+9 x^2+\log (2-x)}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}+\frac {2 \left (324+108 x+9 x^2+\log (2-x)\right )}{(-2+x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}+\frac {108 x \left (324+108 x+9 x^2+\log (2-x)\right )}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}+\frac {18 x^2 \left (324+108 x+9 x^2+\log (2-x)\right )}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}\right ) \, dx\\ &=4 \int \frac {1}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)} \, dx-32 \int \frac {324+108 x+9 x^2+\log (2-x)}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx-64 \int \frac {324+108 x+9 x^2+\log (2-x)}{(-2+x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx-576 \int \frac {x^2 \left (324+108 x+9 x^2+\log (2-x)\right )}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx-3456 \int \frac {x \left (324+108 x+9 x^2+\log (2-x)\right )}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 48, normalized size = 2.00 \begin {gather*} \frac {4 x}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+72 (6+x)^2 \log (2-x)+4 \log ^2(2-x)} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-3359384 + 1669324*x + 556416*x^2 - 155808*x^3 - 54432*x^4 - 3888*x^5 + (-20736 + 10336*x + 576*x^2
- 288*x^3)*Log[2 - x] + (-32 + 16*x)*Log[2 - x]^2)/(-352670651858 - 293870933783*x - 39176763264*x^2 + 457144
97472*x^3 + 26665854480*x^4 + 6983855640*x^5 + 1058158080*x^6 + 95738112*x^7 + 4828896*x^8 + 104976*x^9 + (-43
53761664 - 2176749504*x + 362824416*x^2 + 503887536*x^3 + 151165440*x^4 + 21835008*x^5 + 1586304*x^6 + 46656*x
^7)*Log[2 - x] + (-20155696 - 3359080*x + 3359232*x^2 + 1306368*x^3 + 171072*x^4 + 7776*x^5)*Log[2 - x]^2 + (-
41472 + 6912*x + 5760*x^2 + 576*x^3)*Log[2 - x]^3 + (-32 + 16*x)*Log[2 - x]^4),x]
[Out]
(4*x)/(419923 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 72*(6 + x)^2*Log[2 - x] + 4*Log[2 - x]^2)
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fricas [B] time = 1.24, size = 51, normalized size = 2.12 \begin {gather*} \frac {4 \, x}{324 \, x^{4} + 7776 \, x^{3} + 69984 \, x^{2} + 72 \, {\left (x^{2} + 12 \, x + 36\right )} \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 279936 \, x + 419923} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((16*x-32)*log(2-x)^2+(-288*x^3+576*x^2+10336*x-20736)*log(2-x)-3888*x^5-54432*x^4-155808*x^3+556416
*x^2+1669324*x-3359384)/((16*x-32)*log(2-x)^4+(576*x^3+5760*x^2+6912*x-41472)*log(2-x)^3+(7776*x^5+171072*x^4+
1306368*x^3+3359232*x^2-3359080*x-20155696)*log(2-x)^2+(46656*x^7+1586304*x^6+21835008*x^5+151165440*x^4+50388
7536*x^3+362824416*x^2-2176749504*x-4353761664)*log(2-x)+104976*x^9+4828896*x^8+95738112*x^7+1058158080*x^6+69
83855640*x^5+26665854480*x^4+45714497472*x^3-39176763264*x^2-293870933783*x-352670651858),x, algorithm="fricas
")
[Out]
4*x/(324*x^4 + 7776*x^3 + 69984*x^2 + 72*(x^2 + 12*x + 36)*log(-x + 2) + 4*log(-x + 2)^2 + 279936*x + 419923)
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giac [B] time = 0.75, size = 63, normalized size = 2.62 \begin {gather*} \frac {4 \, x}{324 \, x^{4} + 7776 \, x^{3} + 72 \, x^{2} \log \left (-x + 2\right ) + 69984 \, x^{2} + 864 \, x \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 279936 \, x + 2592 \, \log \left (-x + 2\right ) + 419923} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((16*x-32)*log(2-x)^2+(-288*x^3+576*x^2+10336*x-20736)*log(2-x)-3888*x^5-54432*x^4-155808*x^3+556416
*x^2+1669324*x-3359384)/((16*x-32)*log(2-x)^4+(576*x^3+5760*x^2+6912*x-41472)*log(2-x)^3+(7776*x^5+171072*x^4+
1306368*x^3+3359232*x^2-3359080*x-20155696)*log(2-x)^2+(46656*x^7+1586304*x^6+21835008*x^5+151165440*x^4+50388
7536*x^3+362824416*x^2-2176749504*x-4353761664)*log(2-x)+104976*x^9+4828896*x^8+95738112*x^7+1058158080*x^6+69
83855640*x^5+26665854480*x^4+45714497472*x^3-39176763264*x^2-293870933783*x-352670651858),x, algorithm="giac")
[Out]
4*x/(324*x^4 + 7776*x^3 + 72*x^2*log(-x + 2) + 69984*x^2 + 864*x*log(-x + 2) + 4*log(-x + 2)^2 + 279936*x + 25
92*log(-x + 2) + 419923)
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maple [B] time = 0.04, size = 64, normalized size = 2.67
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\(\frac {4 x}{324 x^{4}+72 \ln \left (2-x \right ) x^{2}+7776 x^{3}+4 \ln \left (2-x \right )^{2}+864 x \ln \left (2-x \right )+69984 x^{2}+2592 \ln \left (2-x \right )+279936 x +419923}\) |
\(64\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((16*x-32)*ln(2-x)^2+(-288*x^3+576*x^2+10336*x-20736)*ln(2-x)-3888*x^5-54432*x^4-155808*x^3+556416*x^2+166
9324*x-3359384)/((16*x-32)*ln(2-x)^4+(576*x^3+5760*x^2+6912*x-41472)*ln(2-x)^3+(7776*x^5+171072*x^4+1306368*x^
3+3359232*x^2-3359080*x-20155696)*ln(2-x)^2+(46656*x^7+1586304*x^6+21835008*x^5+151165440*x^4+503887536*x^3+36
2824416*x^2-2176749504*x-4353761664)*ln(2-x)+104976*x^9+4828896*x^8+95738112*x^7+1058158080*x^6+6983855640*x^5
+26665854480*x^4+45714497472*x^3-39176763264*x^2-293870933783*x-352670651858),x,method=_RETURNVERBOSE)
[Out]
4*x/(324*x^4+72*ln(2-x)*x^2+7776*x^3+4*ln(2-x)^2+864*x*ln(2-x)+69984*x^2+2592*ln(2-x)+279936*x+419923)
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maxima [B] time = 0.51, size = 51, normalized size = 2.12 \begin {gather*} \frac {4 \, x}{324 \, x^{4} + 7776 \, x^{3} + 69984 \, x^{2} + 72 \, {\left (x^{2} + 12 \, x + 36\right )} \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 279936 \, x + 419923} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((16*x-32)*log(2-x)^2+(-288*x^3+576*x^2+10336*x-20736)*log(2-x)-3888*x^5-54432*x^4-155808*x^3+556416
*x^2+1669324*x-3359384)/((16*x-32)*log(2-x)^4+(576*x^3+5760*x^2+6912*x-41472)*log(2-x)^3+(7776*x^5+171072*x^4+
1306368*x^3+3359232*x^2-3359080*x-20155696)*log(2-x)^2+(46656*x^7+1586304*x^6+21835008*x^5+151165440*x^4+50388
7536*x^3+362824416*x^2-2176749504*x-4353761664)*log(2-x)+104976*x^9+4828896*x^8+95738112*x^7+1058158080*x^6+69
83855640*x^5+26665854480*x^4+45714497472*x^3-39176763264*x^2-293870933783*x-352670651858),x, algorithm="maxima
")
[Out]
4*x/(324*x^4 + 7776*x^3 + 69984*x^2 + 72*(x^2 + 12*x + 36)*log(-x + 2) + 4*log(-x + 2)^2 + 279936*x + 419923)
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1669324\,x+{\ln \left (2-x\right )}^2\,\left (16\,x-32\right )+\ln \left (2-x\right )\,\left (-288\,x^3+576\,x^2+10336\,x-20736\right )+556416\,x^2-155808\,x^3-54432\,x^4-3888\,x^5-3359384}{{\ln \left (2-x\right )}^3\,\left (576\,x^3+5760\,x^2+6912\,x-41472\right )-293870933783\,x+\ln \left (2-x\right )\,\left (46656\,x^7+1586304\,x^6+21835008\,x^5+151165440\,x^4+503887536\,x^3+362824416\,x^2-2176749504\,x-4353761664\right )+{\ln \left (2-x\right )}^2\,\left (7776\,x^5+171072\,x^4+1306368\,x^3+3359232\,x^2-3359080\,x-20155696\right )+{\ln \left (2-x\right )}^4\,\left (16\,x-32\right )-39176763264\,x^2+45714497472\,x^3+26665854480\,x^4+6983855640\,x^5+1058158080\,x^6+95738112\,x^7+4828896\,x^8+104976\,x^9-352670651858} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((1669324*x + log(2 - x)^2*(16*x - 32) + log(2 - x)*(10336*x + 576*x^2 - 288*x^3 - 20736) + 556416*x^2 - 15
5808*x^3 - 54432*x^4 - 3888*x^5 - 3359384)/(log(2 - x)^3*(6912*x + 5760*x^2 + 576*x^3 - 41472) - 293870933783*
x + log(2 - x)*(362824416*x^2 - 2176749504*x + 503887536*x^3 + 151165440*x^4 + 21835008*x^5 + 1586304*x^6 + 46
656*x^7 - 4353761664) + log(2 - x)^2*(3359232*x^2 - 3359080*x + 1306368*x^3 + 171072*x^4 + 7776*x^5 - 20155696
) + log(2 - x)^4*(16*x - 32) - 39176763264*x^2 + 45714497472*x^3 + 26665854480*x^4 + 6983855640*x^5 + 10581580
80*x^6 + 95738112*x^7 + 4828896*x^8 + 104976*x^9 - 352670651858),x)
[Out]
int((1669324*x + log(2 - x)^2*(16*x - 32) + log(2 - x)*(10336*x + 576*x^2 - 288*x^3 - 20736) + 556416*x^2 - 15
5808*x^3 - 54432*x^4 - 3888*x^5 - 3359384)/(log(2 - x)^3*(6912*x + 5760*x^2 + 576*x^3 - 41472) - 293870933783*
x + log(2 - x)*(362824416*x^2 - 2176749504*x + 503887536*x^3 + 151165440*x^4 + 21835008*x^5 + 1586304*x^6 + 46
656*x^7 - 4353761664) + log(2 - x)^2*(3359232*x^2 - 3359080*x + 1306368*x^3 + 171072*x^4 + 7776*x^5 - 20155696
) + log(2 - x)^4*(16*x - 32) - 39176763264*x^2 + 45714497472*x^3 + 26665854480*x^4 + 6983855640*x^5 + 10581580
80*x^6 + 95738112*x^7 + 4828896*x^8 + 104976*x^9 - 352670651858), x)
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sympy [B] time = 0.31, size = 46, normalized size = 1.92 \begin {gather*} \frac {4 x}{324 x^{4} + 7776 x^{3} + 69984 x^{2} + 279936 x + \left (72 x^{2} + 864 x + 2592\right ) \log {\left (2 - x \right )} + 4 \log {\left (2 - x \right )}^{2} + 419923} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((16*x-32)*ln(2-x)**2+(-288*x**3+576*x**2+10336*x-20736)*ln(2-x)-3888*x**5-54432*x**4-155808*x**3+55
6416*x**2+1669324*x-3359384)/((16*x-32)*ln(2-x)**4+(576*x**3+5760*x**2+6912*x-41472)*ln(2-x)**3+(7776*x**5+171
072*x**4+1306368*x**3+3359232*x**2-3359080*x-20155696)*ln(2-x)**2+(46656*x**7+1586304*x**6+21835008*x**5+15116
5440*x**4+503887536*x**3+362824416*x**2-2176749504*x-4353761664)*ln(2-x)+104976*x**9+4828896*x**8+95738112*x**
7+1058158080*x**6+6983855640*x**5+26665854480*x**4+45714497472*x**3-39176763264*x**2-293870933783*x-3526706518
58),x)
[Out]
4*x/(324*x**4 + 7776*x**3 + 69984*x**2 + 279936*x + (72*x**2 + 864*x + 2592)*log(2 - x) + 4*log(2 - x)**2 + 41
9923)
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