Optimal. Leaf size=80 \[ -\frac{54675 x^7}{56}-\frac{268515 x^6}{32}-\frac{2798631 x^5}{80}-\frac{12299769 x^4}{128}-\frac{25895367 x^3}{128}-\frac{190742391 x^2}{512}-\frac{48280011 x}{64}-\frac{389535839}{1024 (1-2 x)}+\frac{99648703}{2048 (1-2 x)^2}-\frac{84589631}{128} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.104701, 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 \[ -\frac{54675 x^7}{56}-\frac{268515 x^6}{32}-\frac{2798631 x^5}{80}-\frac{12299769 x^4}{128}-\frac{25895367 x^3}{128}-\frac{190742391 x^2}{512}-\frac{48280011 x}{64}-\frac{389535839}{1024 (1-2 x)}+\frac{99648703}{2048 (1-2 x)^2}-\frac{84589631}{128} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{54675 x^{7}}{56} - \frac{268515 x^{6}}{32} - \frac{2798631 x^{5}}{80} - \frac{12299769 x^{4}}{128} - \frac{25895367 x^{3}}{128} - \frac{84589631 \log{\left (- 2 x + 1 \right )}}{128} + \int \left (- \frac{48280011}{64}\right )\, dx - \frac{190742391 \int x\, dx}{256} - \frac{389535839}{1024 \left (- 2 x + 1\right )} + \frac{99648703}{2048 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**7*(3+5*x)**2/(1-2*x)**3,x)
[Out]
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Mathematica [A] time = 0.0381554, size = 71, normalized size = 0.89 \[ -\frac{34992000 x^9+265744800 x^8+961797888 x^7+2265332832 x^6+4120214112 x^5+6962248440 x^4+15497514480 x^3-41720946264 x^2+17964456304 x+5921274170 (1-2 x)^2 \log (1-2 x)-1533057471}{8960 (1-2 x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^7*(3 + 5*x)^2)/(1 - 2*x)^3,x]
[Out]
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Maple [A] time = 0.01, size = 61, normalized size = 0.8 \[ -{\frac{54675\,{x}^{7}}{56}}-{\frac{268515\,{x}^{6}}{32}}-{\frac{2798631\,{x}^{5}}{80}}-{\frac{12299769\,{x}^{4}}{128}}-{\frac{25895367\,{x}^{3}}{128}}-{\frac{190742391\,{x}^{2}}{512}}-{\frac{48280011\,x}{64}}+{\frac{99648703}{2048\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{389535839}{-1024+2048\,x}}-{\frac{84589631\,\ln \left ( -1+2\,x \right ) }{128}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^7*(3+5*x)^2/(1-2*x)^3,x)
[Out]
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Maxima [A] time = 1.31968, size = 82, normalized size = 1.02 \[ -\frac{54675}{56} \, x^{7} - \frac{268515}{32} \, x^{6} - \frac{2798631}{80} \, x^{5} - \frac{12299769}{128} \, x^{4} - \frac{25895367}{128} \, x^{3} - \frac{190742391}{512} \, x^{2} - \frac{48280011}{64} \, x + \frac{9058973 \,{\left (172 \, x - 75\right )}}{2048 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{84589631}{128} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^7/(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216246, size = 104, normalized size = 1.3 \[ -\frac{279936000 \, x^{9} + 2125958400 \, x^{8} + 7694383104 \, x^{7} + 18122662656 \, x^{6} + 32961712896 \, x^{5} + 55697987520 \, x^{4} + 123980115840 \, x^{3} - 189590514540 \, x^{2} + 47370193360 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 461405140 \, x + 23779804125}{71680 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^7/(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.35496, size = 70, normalized size = 0.88 \[ - \frac{54675 x^{7}}{56} - \frac{268515 x^{6}}{32} - \frac{2798631 x^{5}}{80} - \frac{12299769 x^{4}}{128} - \frac{25895367 x^{3}}{128} - \frac{190742391 x^{2}}{512} - \frac{48280011 x}{64} + \frac{1558143356 x - 679422975}{8192 x^{2} - 8192 x + 2048} - \frac{84589631 \log{\left (2 x - 1 \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**7*(3+5*x)**2/(1-2*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.208777, size = 77, normalized size = 0.96 \[ -\frac{54675}{56} \, x^{7} - \frac{268515}{32} \, x^{6} - \frac{2798631}{80} \, x^{5} - \frac{12299769}{128} \, x^{4} - \frac{25895367}{128} \, x^{3} - \frac{190742391}{512} \, x^{2} - \frac{48280011}{64} \, x + \frac{9058973 \,{\left (172 \, x - 75\right )}}{2048 \,{\left (2 \, x - 1\right )}^{2}} - \frac{84589631}{128} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^7/(2*x - 1)^3,x, algorithm="giac")
[Out]