Optimal. Leaf size=75 \[ -\frac{103455}{3 x+2}-\frac{33275}{5 x+3}-\frac{8349}{(3 x+2)^2}-\frac{847}{(3 x+2)^3}-\frac{784}{9 (3 x+2)^4}-\frac{343}{45 (3 x+2)^5}+617100 \log (3 x+2)-617100 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.093444, antiderivative size = 75, 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 \[ -\frac{103455}{3 x+2}-\frac{33275}{5 x+3}-\frac{8349}{(3 x+2)^2}-\frac{847}{(3 x+2)^3}-\frac{784}{9 (3 x+2)^4}-\frac{343}{45 (3 x+2)^5}+617100 \log (3 x+2)-617100 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 5.92648, size = 66, normalized size = 0.88 \[ 617100 \log{\left (3 x + 2 \right )} - 617100 \log{\left (5 x + 3 \right )} - \frac{33275}{5 x + 3} - \frac{103455}{3 x + 2} - \frac{8349}{\left (3 x + 2\right )^{2}} - \frac{847}{\left (3 x + 2\right )^{3}} - \frac{784}{9 \left (3 x + 2\right )^{4}} - \frac{343}{45 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3/(2+3*x)**6/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0994562, size = 62, normalized size = 0.83 \[ -\frac{2249329500 x^5+7422787350 x^4+9795413430 x^3+6461351715 x^2+2130399775 x+280877649}{45 (3 x+2)^5 (5 x+3)}+617100 \log (5 (3 x+2))-617100 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3/((2 + 3*x)^6*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.016, size = 72, normalized size = 1. \[ -{\frac{343}{45\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{784}{9\, \left ( 2+3\,x \right ) ^{4}}}-847\, \left ( 2+3\,x \right ) ^{-3}-8349\, \left ( 2+3\,x \right ) ^{-2}-103455\, \left ( 2+3\,x \right ) ^{-1}-33275\, \left ( 3+5\,x \right ) ^{-1}+617100\,\ln \left ( 2+3\,x \right ) -617100\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3/(2+3*x)^6/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.36055, size = 103, normalized size = 1.37 \[ -\frac{2249329500 \, x^{5} + 7422787350 \, x^{4} + 9795413430 \, x^{3} + 6461351715 \, x^{2} + 2130399775 \, x + 280877649}{45 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} - 617100 \, \log \left (5 \, x + 3\right ) + 617100 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)^6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207945, size = 182, normalized size = 2.43 \[ -\frac{2249329500 \, x^{5} + 7422787350 \, x^{4} + 9795413430 \, x^{3} + 6461351715 \, x^{2} + 27769500 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (5 \, x + 3\right ) - 27769500 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )} \log \left (3 \, x + 2\right ) + 2130399775 \, x + 280877649}{45 \,{\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.585638, size = 71, normalized size = 0.95 \[ - \frac{2249329500 x^{5} + 7422787350 x^{4} + 9795413430 x^{3} + 6461351715 x^{2} + 2130399775 x + 280877649}{54675 x^{6} + 215055 x^{5} + 352350 x^{4} + 307800 x^{3} + 151200 x^{2} + 39600 x + 4320} - 617100 \log{\left (x + \frac{3}{5} \right )} + 617100 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3/(2+3*x)**6/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.211882, size = 103, normalized size = 1.37 \[ -\frac{33275}{5 \, x + 3} + \frac{25 \,{\left (\frac{13068279}{5 \, x + 3} + \frac{7369449}{{\left (5 \, x + 3\right )}^{2}} + \frac{1895648}{{\left (5 \, x + 3\right )}^{3}} + \frac{190707}{{\left (5 \, x + 3\right )}^{4}} + 8846550\right )}}{{\left (\frac{1}{5 \, x + 3} + 3\right )}^{5}} + 617100 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)^2*(3*x + 2)^6),x, algorithm="giac")
[Out]