Optimal. Leaf size=76 \[ \frac{32805 x^8}{32}+\frac{56862 x^7}{7}+\frac{976617 x^6}{32}+\frac{5859459 x^5}{80}+\frac{32991057 x^4}{256}+\frac{5892813 x^3}{32}+\frac{122887143 x^2}{512}+\frac{91609881 x}{256}+\frac{63412811}{1024 (1-2 x)}+\frac{246239357 \log (1-2 x)}{1024} \]
[Out]
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Rubi [A] time = 0.0900259, antiderivative size = 76, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{32805 x^8}{32}+\frac{56862 x^7}{7}+\frac{976617 x^6}{32}+\frac{5859459 x^5}{80}+\frac{32991057 x^4}{256}+\frac{5892813 x^3}{32}+\frac{122887143 x^2}{512}+\frac{91609881 x}{256}+\frac{63412811}{1024 (1-2 x)}+\frac{246239357 \log (1-2 x)}{1024} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{32805 x^{8}}{32} + \frac{56862 x^{7}}{7} + \frac{976617 x^{6}}{32} + \frac{5859459 x^{5}}{80} + \frac{32991057 x^{4}}{256} + \frac{5892813 x^{3}}{32} + \frac{246239357 \log{\left (- 2 x + 1 \right )}}{1024} + \int \frac{91609881}{256}\, dx + \frac{122887143 \int x\, dx}{256} + \frac{63412811}{1024 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**8*(3+5*x)/(1-2*x)**2,x)
[Out]
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Mathematica [A] time = 0.0269714, size = 69, normalized size = 0.91 \[ \frac{587865600 x^9+4364202240 x^8+15171909120 x^7+33250113792 x^6+52899666624 x^5+68649225120 x^4+84833995680 x^3+136389333360 x^2-259057842186 x+68947019960 (2 x-1) \log (1-2 x)+60471800653}{286720 (2 x-1)} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 57, normalized size = 0.8 \[{\frac{32805\,{x}^{8}}{32}}+{\frac{56862\,{x}^{7}}{7}}+{\frac{976617\,{x}^{6}}{32}}+{\frac{5859459\,{x}^{5}}{80}}+{\frac{32991057\,{x}^{4}}{256}}+{\frac{5892813\,{x}^{3}}{32}}+{\frac{122887143\,{x}^{2}}{512}}+{\frac{91609881\,x}{256}}-{\frac{63412811}{-1024+2048\,x}}+{\frac{246239357\,\ln \left ( -1+2\,x \right ) }{1024}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^8*(3+5*x)/(1-2*x)^2,x)
[Out]
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Maxima [A] time = 1.34686, size = 76, normalized size = 1. \[ \frac{32805}{32} \, x^{8} + \frac{56862}{7} \, x^{7} + \frac{976617}{32} \, x^{6} + \frac{5859459}{80} \, x^{5} + \frac{32991057}{256} \, x^{4} + \frac{5892813}{32} \, x^{3} + \frac{122887143}{512} \, x^{2} + \frac{91609881}{256} \, x - \frac{63412811}{1024 \,{\left (2 \, x - 1\right )}} + \frac{246239357}{1024} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^8/(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214907, size = 90, normalized size = 1.18 \[ \frac{73483200 \, x^{9} + 545525280 \, x^{8} + 1896488640 \, x^{7} + 4156264224 \, x^{6} + 6612458328 \, x^{5} + 8581153140 \, x^{4} + 10604249460 \, x^{3} + 17048666670 \, x^{2} + 8618377495 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 12825383340 \, x - 2219448385}{35840 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^8/(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.25071, size = 68, normalized size = 0.89 \[ \frac{32805 x^{8}}{32} + \frac{56862 x^{7}}{7} + \frac{976617 x^{6}}{32} + \frac{5859459 x^{5}}{80} + \frac{32991057 x^{4}}{256} + \frac{5892813 x^{3}}{32} + \frac{122887143 x^{2}}{512} + \frac{91609881 x}{256} + \frac{246239357 \log{\left (2 x - 1 \right )}}{1024} - \frac{63412811}{2048 x - 1024} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**8*(3+5*x)/(1-2*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.208937, size = 138, normalized size = 1.82 \[ \frac{3}{286720} \,{\left (2 \, x - 1\right )}^{8}{\left (\frac{9127080}{2 \, x - 1} + \frac{98748720}{{\left (2 \, x - 1\right )}^{2}} + \frac{641009376}{{\left (2 \, x - 1\right )}^{3}} + \frac{2786264460}{{\left (2 \, x - 1\right )}^{4}} + \frac{8611906800}{{\left (2 \, x - 1\right )}^{5}} + \frac{19962682320}{{\left (2 \, x - 1\right )}^{6}} + \frac{39661830880}{{\left (2 \, x - 1\right )}^{7}} + 382725\right )} - \frac{63412811}{1024 \,{\left (2 \, x - 1\right )}} - \frac{246239357}{1024} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^8/(2*x - 1)^2,x, algorithm="giac")
[Out]