Integrand size = 223, antiderivative size = 24 \[ \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx=\frac {x}{\frac {19}{4}+\left (9 (6+x)^2+\log (2-x)\right )^2} \] Output:
x/(19/4+(3*(6+x)*(3*x+18)+ln(2-x))^2)
Time = 0.06 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.00 \[ \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx=\frac {4 x}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+72 (6+x)^2 \log (2-x)+4 \log ^2(2-x)} \] Input:
Integrate[(-3359384 + 1669324*x + 556416*x^2 - 155808*x^3 - 54432*x^4 - 38 88*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 + 45714497 472*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 - x]^2 + (-41472 + 6912*x + 5760*x^2 + 576*x^3)*Log[2 - x]^3 + (-32 + 16*x)*Log[2 - x]^4),x]
Output:
(4*x)/(419923 + 279936*x + 69984*x^2 + 7776*x^3 + 324*x^4 + 72*(6 + x)^2*L og[2 - x] + 4*Log[2 - x]^2)
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-3888 x^5-54432 x^4-155808 x^3+556416 x^2+\left (-288 x^3+576 x^2+10336 x-20736\right ) \log (2-x)+1669324 x+(16 x-32) \log ^2(2-x)-3359384}{104976 x^9+4828896 x^8+95738112 x^7+1058158080 x^6+6983855640 x^5+26665854480 x^4+45714497472 x^3-39176763264 x^2+\left (576 x^3+5760 x^2+6912 x-41472\right ) \log ^3(2-x)+\left (7776 x^5+171072 x^4+1306368 x^3+3359232 x^2-3359080 x-20155696\right ) \log ^2(2-x)+\left (46656 x^7+1586304 x^6+21835008 x^5+151165440 x^4+503887536 x^3+362824416 x^2-2176749504 x-4353761664\right ) \log (2-x)-293870933783 x+(16 x-32) \log ^4(2-x)-352670651858} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (972 x^5+13608 x^4+38952 x^3-139104 x^2+8 \left (9 x^3-18 x^2-323 x+648\right ) \log (2-x)-417331 x-4 (x-2) \log ^2(2-x)+839846\right )}{(2-x) \left (324 x^4+7776 x^3+69984 x^2+279936 x+4 \log ^2(2-x)+72 (x+6)^2 \log (2-x)+419923\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int \frac {972 x^5+13608 x^4+38952 x^3-139104 x^2-417331 x+4 (2-x) \log ^2(2-x)+8 \left (9 x^3-18 x^2-323 x+648\right ) \log (2-x)+839846}{(2-x) \left (324 x^4+7776 x^3+69984 x^2+279936 x+4 \log ^2(2-x)+72 (x+6)^2 \log (2-x)+419923\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {1}{324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923}-\frac {8 x \left (18 x^2+72 x-215\right ) \left (9 x^2+108 x+\log (2-x)+324\right )}{(x-2) \left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 \left (-4608 \int \frac {1}{\left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-9216 \int \frac {1}{(x-2) \left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-280944 \int \frac {x}{\left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-140040 \int \frac {x^2}{\left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-23328 \int \frac {x^3}{\left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-1296 \int \frac {x^4}{\left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-8 \int \frac {\log (2-x)}{\left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-16 \int \frac {\log (2-x)}{(x-2) \left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-864 \int \frac {x \log (2-x)}{\left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx-144 \int \frac {x^2 \log (2-x)}{\left (324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923\right )^2}dx+\int \frac {1}{324 x^4+7776 x^3+72 \log (2-x) x^2+69984 x^2+864 \log (2-x) x+279936 x+4 \log ^2(2-x)+2592 \log (2-x)+419923}dx\right )\) |
Input:
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 + 482 8896*x^8 + 104976*x^9 + (-4353761664 - 2176749504*x + 362824416*x^2 + 5038 87536*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 + 7 776*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]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(63\) vs. \(2(25)=50\).
Time = 1.21 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.67
| method | result | size |
| risch | \(\frac {4 x}{324 x^{4}+72 \ln \left (2-x \right ) x^{2}+7776 x^{3}+4 \ln \left (2-x \right )^{2}+864 x \ln \left (2-x \right )+69984 x^{2}+2592 \ln \left (2-x \right )+279936 x +419923}\) | \(64\) |
| parallelrisch | \(\frac {4 x}{324 x^{4}+72 \ln \left (2-x \right ) x^{2}+7776 x^{3}+4 \ln \left (2-x \right )^{2}+864 x \ln \left (2-x \right )+69984 x^{2}+2592 \ln \left (2-x \right )+279936 x +419923}\) | \(64\) |
| derivativedivides | \(\frac {4 x}{324 \left (2-x \right )^{4}-10368 \left (2-x \right )^{3}+72 \ln \left (2-x \right ) \left (2-x \right )^{2}+124416 \left (2-x \right )^{2}-1152 \left (2-x \right ) \ln \left (2-x \right )+4 \ln \left (2-x \right )^{2}+19+663552 x +4608 \ln \left (2-x \right )}\) | \(84\) |
| default | \(\frac {4 x}{324 \left (2-x \right )^{4}-10368 \left (2-x \right )^{3}+72 \ln \left (2-x \right ) \left (2-x \right )^{2}+124416 \left (2-x \right )^{2}-1152 \left (2-x \right ) \ln \left (2-x \right )+4 \ln \left (2-x \right )^{2}+19+663552 x +4608 \ln \left (2-x \right )}\) | \(84\) |
Input:
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+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+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+362824416*x^2-2176749504*x-4353761664)*ln( 2-x)+104976*x^9+4828896*x^8+95738112*x^7+1058158080*x^6+6983855640*x^5+266 65854480*x^4+45714497472*x^3-39176763264*x^2-293870933783*x-352670651858), x,method=_RETURNVERBOSE)
Output:
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+2 592*ln(2-x)+279936*x+419923)
Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (25) = 50\).
Time = 0.06 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12 \[ \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx=\frac {4 \, x}{324 \, x^{4} + 7776 \, x^{3} + 69984 \, x^{2} + 72 \, {\left (x^{2} + 12 \, x + 36\right )} \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 279936 \, x + 419923} \] Input:
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+13 06368*x^3+3359232*x^2-3359080*x-20155696)*log(2-x)^2+(46656*x^7+1586304*x^ 6+21835008*x^5+151165440*x^4+503887536*x^3+362824416*x^2-2176749504*x-4353 761664)*log(2-x)+104976*x^9+4828896*x^8+95738112*x^7+1058158080*x^6+698385 5640*x^5+26665854480*x^4+45714497472*x^3-39176763264*x^2-293870933783*x-35 2670651858),x, algorithm="fricas")
Output:
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)
Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (17) = 34\).
Time = 0.16 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.92 \[ \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx=\frac {4 x}{324 x^{4} + 7776 x^{3} + 69984 x^{2} + 279936 x + \left (72 x^{2} + 864 x + 2592\right ) \log {\left (2 - x \right )} + 4 \log {\left (2 - x \right )}^{2} + 419923} \] Input:
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+556416*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+17107 2*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+362824416*x**2- 2176749504*x-4353761664)*ln(2-x)+104976*x**9+4828896*x**8+95738112*x**7+10 58158080*x**6+6983855640*x**5+26665854480*x**4+45714497472*x**3-3917676326 4*x**2-293870933783*x-352670651858),x)
Output:
4*x/(324*x**4 + 7776*x**3 + 69984*x**2 + 279936*x + (72*x**2 + 864*x + 259 2)*log(2 - x) + 4*log(2 - x)**2 + 419923)
Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (25) = 50\).
Time = 0.09 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12 \[ \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx=\frac {4 \, x}{324 \, x^{4} + 7776 \, x^{3} + 69984 \, x^{2} + 72 \, {\left (x^{2} + 12 \, x + 36\right )} \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 279936 \, x + 419923} \] Input:
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+13 06368*x^3+3359232*x^2-3359080*x-20155696)*log(2-x)^2+(46656*x^7+1586304*x^ 6+21835008*x^5+151165440*x^4+503887536*x^3+362824416*x^2-2176749504*x-4353 761664)*log(2-x)+104976*x^9+4828896*x^8+95738112*x^7+1058158080*x^6+698385 5640*x^5+26665854480*x^4+45714497472*x^3-39176763264*x^2-293870933783*x-35 2670651858),x, algorithm="maxima")
Output:
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)
Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (25) = 50\).
Time = 0.21 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.04 \[ \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx=\frac {4 \, x}{324 \, {\left (x - 2\right )}^{4} + 10368 \, {\left (x - 2\right )}^{3} + 72 \, {\left (x - 2\right )}^{2} \log \left (-x + 2\right ) + 124416 \, {\left (x - 2\right )}^{2} + 1152 \, {\left (x - 2\right )} \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 663552 \, x + 4608 \, \log \left (-x + 2\right ) + 19} \] Input:
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+13 06368*x^3+3359232*x^2-3359080*x-20155696)*log(2-x)^2+(46656*x^7+1586304*x^ 6+21835008*x^5+151165440*x^4+503887536*x^3+362824416*x^2-2176749504*x-4353 761664)*log(2-x)+104976*x^9+4828896*x^8+95738112*x^7+1058158080*x^6+698385 5640*x^5+26665854480*x^4+45714497472*x^3-39176763264*x^2-293870933783*x-35 2670651858),x, algorithm="giac")
Output:
4*x/(324*(x - 2)^4 + 10368*(x - 2)^3 + 72*(x - 2)^2*log(-x + 2) + 124416*( x - 2)^2 + 1152*(x - 2)*log(-x + 2) + 4*log(-x + 2)^2 + 663552*x + 4608*lo g(-x + 2) + 19)
Timed out. \[ \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx=\int \frac {1669324\,x+{\ln \left (2-x\right )}^2\,\left (16\,x-32\right )+\ln \left (2-x\right )\,\left (-288\,x^3+576\,x^2+10336\,x-20736\right )+556416\,x^2-155808\,x^3-54432\,x^4-3888\,x^5-3359384}{{\ln \left (2-x\right )}^3\,\left (576\,x^3+5760\,x^2+6912\,x-41472\right )-293870933783\,x+\ln \left (2-x\right )\,\left (46656\,x^7+1586304\,x^6+21835008\,x^5+151165440\,x^4+503887536\,x^3+362824416\,x^2-2176749504\,x-4353761664\right )+{\ln \left (2-x\right )}^2\,\left (7776\,x^5+171072\,x^4+1306368\,x^3+3359232\,x^2-3359080\,x-20155696\right )+{\ln \left (2-x\right )}^4\,\left (16\,x-32\right )-39176763264\,x^2+45714497472\,x^3+26665854480\,x^4+6983855640\,x^5+1058158080\,x^6+95738112\,x^7+4828896\,x^8+104976\,x^9-352670651858} \,d x \] Input:
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 - 155808*x^3 - 54432*x^4 - 3888*x^5 - 3359 384)/(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 + 46656*x^7 - 4353761664) + log(2 - x)^2*(33 59232*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 + 1058158080*x^6 + 95738112*x^7 + 4828896*x^8 + 1049 76*x^9 - 352670651858),x)
Output:
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 - 155808*x^3 - 54432*x^4 - 3888*x^5 - 3359 384)/(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 + 46656*x^7 - 4353761664) + log(2 - x)^2*(33 59232*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 + 1058158080*x^6 + 95738112*x^7 + 4828896*x^8 + 1049 76*x^9 - 352670651858), x)
\[ \int \frac {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx=\text {too large to display} \] Input:
int(((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+2183 5008*x^5+151165440*x^4+503887536*x^3+362824416*x^2-2176749504*x-4353761664 )*log(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-35267065 1858),x)
Output:
4*( - 8*int(log( - x + 2)**2/(16*log( - x + 2)**4*x - 32*log( - x + 2)**4 + 576*log( - x + 2)**3*x**3 + 5760*log( - x + 2)**3*x**2 + 6912*log( - x + 2)**3*x - 41472*log( - x + 2)**3 + 7776*log( - x + 2)**2*x**5 + 171072*lo g( - x + 2)**2*x**4 + 1306368*log( - x + 2)**2*x**3 + 3359232*log( - x + 2 )**2*x**2 - 3359080*log( - x + 2)**2*x - 20155696*log( - x + 2)**2 + 46656 *log( - x + 2)*x**7 + 1586304*log( - x + 2)*x**6 + 21835008*log( - x + 2)* x**5 + 151165440*log( - x + 2)*x**4 + 503887536*log( - x + 2)*x**3 + 36282 4416*log( - x + 2)*x**2 - 2176749504*log( - x + 2)*x - 4353761664*log( - x + 2) + 104976*x**9 + 4828896*x**8 + 95738112*x**7 + 1058158080*x**6 + 698 3855640*x**5 + 26665854480*x**4 + 45714497472*x**3 - 39176763264*x**2 - 29 3870933783*x - 352670651858),x) - 972*int(x**5/(16*log( - x + 2)**4*x - 32 *log( - x + 2)**4 + 576*log( - x + 2)**3*x**3 + 5760*log( - x + 2)**3*x**2 + 6912*log( - x + 2)**3*x - 41472*log( - x + 2)**3 + 7776*log( - x + 2)** 2*x**5 + 171072*log( - x + 2)**2*x**4 + 1306368*log( - x + 2)**2*x**3 + 33 59232*log( - x + 2)**2*x**2 - 3359080*log( - x + 2)**2*x - 20155696*log( - x + 2)**2 + 46656*log( - x + 2)*x**7 + 1586304*log( - x + 2)*x**6 + 21835 008*log( - x + 2)*x**5 + 151165440*log( - x + 2)*x**4 + 503887536*log( - x + 2)*x**3 + 362824416*log( - x + 2)*x**2 - 2176749504*log( - x + 2)*x - 4 353761664*log( - x + 2) + 104976*x**9 + 4828896*x**8 + 95738112*x**7 + 105 8158080*x**6 + 6983855640*x**5 + 26665854480*x**4 + 45714497472*x**3 - ...