Optimal. Leaf size=80 \[ -\frac{91125 x^7}{56}-\frac{443475 x^6}{32}-\frac{229149 x^5}{4}-\frac{19986237 x^4}{128}-\frac{41793093 x^3}{128}-\frac{306103815 x^2}{512}-\frac{308539921 x}{256}-\frac{616195041}{1024 (1-2 x)}+\frac{156590819}{2048 (1-2 x)^2}-\frac{33674025}{32} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.1037, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{91125 x^7}{56}-\frac{443475 x^6}{32}-\frac{229149 x^5}{4}-\frac{19986237 x^4}{128}-\frac{41793093 x^3}{128}-\frac{306103815 x^2}{512}-\frac{308539921 x}{256}-\frac{616195041}{1024 (1-2 x)}+\frac{156590819}{2048 (1-2 x)^2}-\frac{33674025}{32} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{91125 x^{7}}{56} - \frac{443475 x^{6}}{32} - \frac{229149 x^{5}}{4} - \frac{19986237 x^{4}}{128} - \frac{41793093 x^{3}}{128} - \frac{33674025 \log{\left (- 2 x + 1 \right )}}{32} + \int \left (- \frac{308539921}{256}\right )\, dx - \frac{306103815 \int x\, dx}{256} - \frac{616195041}{1024 \left (- 2 x + 1\right )} + \frac{156590819}{2048 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6*(3+5*x)**3/(1-2*x)**3,x)
[Out]
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Mathematica [A] time = 0.0415869, size = 71, normalized size = 0.89 \[ -\frac{23328000 x^9+175348800 x^8+628425216 x^7+1466857728 x^6+2647685376 x^5+4449695040 x^4+9877535360 x^3-26671311588 x^2+11541996324 x+3771490800 (1-2 x)^2 \log (1-2 x)-1001301969}{3584 (1-2 x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^6*(3 + 5*x)^3)/(1 - 2*x)^3,x]
[Out]
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Maple [A] time = 0.011, size = 61, normalized size = 0.8 \[ -{\frac{91125\,{x}^{7}}{56}}-{\frac{443475\,{x}^{6}}{32}}-{\frac{229149\,{x}^{5}}{4}}-{\frac{19986237\,{x}^{4}}{128}}-{\frac{41793093\,{x}^{3}}{128}}-{\frac{306103815\,{x}^{2}}{512}}-{\frac{308539921\,x}{256}}+{\frac{156590819}{2048\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{616195041}{-1024+2048\,x}}-{\frac{33674025\,\ln \left ( -1+2\,x \right ) }{32}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6*(3+5*x)^3/(1-2*x)^3,x)
[Out]
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Maxima [A] time = 1.34841, size = 82, normalized size = 1.02 \[ -\frac{91125}{56} \, x^{7} - \frac{443475}{32} \, x^{6} - \frac{229149}{4} \, x^{5} - \frac{19986237}{128} \, x^{4} - \frac{41793093}{128} \, x^{3} - \frac{306103815}{512} \, x^{2} - \frac{308539921}{256} \, x + \frac{2033647 \,{\left (1212 \, x - 529\right )}}{2048 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{33674025}{32} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^6/(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205881, size = 104, normalized size = 1.3 \[ -\frac{93312000 \, x^{9} + 701395200 \, x^{8} + 2513700864 \, x^{7} + 5867430912 \, x^{6} + 10590741504 \, x^{5} + 17798780160 \, x^{4} + 39510141440 \, x^{3} - 60542035484 \, x^{2} + 15085963200 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 24774428 \, x + 7530594841}{14336 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^6/(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.350839, size = 70, normalized size = 0.88 \[ - \frac{91125 x^{7}}{56} - \frac{443475 x^{6}}{32} - \frac{229149 x^{5}}{4} - \frac{19986237 x^{4}}{128} - \frac{41793093 x^{3}}{128} - \frac{306103815 x^{2}}{512} - \frac{308539921 x}{256} + \frac{2464780164 x - 1075799263}{8192 x^{2} - 8192 x + 2048} - \frac{33674025 \log{\left (2 x - 1 \right )}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**6*(3+5*x)**3/(1-2*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.224172, size = 77, normalized size = 0.96 \[ -\frac{91125}{56} \, x^{7} - \frac{443475}{32} \, x^{6} - \frac{229149}{4} \, x^{5} - \frac{19986237}{128} \, x^{4} - \frac{41793093}{128} \, x^{3} - \frac{306103815}{512} \, x^{2} - \frac{308539921}{256} \, x + \frac{2033647 \,{\left (1212 \, x - 529\right )}}{2048 \,{\left (2 \, x - 1\right )}^{2}} - \frac{33674025}{32} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^6/(2*x - 1)^3,x, algorithm="giac")
[Out]