Optimal. Leaf size=45 \[ -\frac{20}{243 (3 x+2)^3}+\frac{4}{9 (3 x+2)^4}-\frac{91}{135 (3 x+2)^5}+\frac{49}{486 (3 x+2)^6} \]
[Out]
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Rubi [A] time = 0.0480717, antiderivative size = 45, 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 \[ -\frac{20}{243 (3 x+2)^3}+\frac{4}{9 (3 x+2)^4}-\frac{91}{135 (3 x+2)^5}+\frac{49}{486 (3 x+2)^6} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^7,x]
[Out]
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Rubi in Sympy [A] time = 8.17168, size = 39, normalized size = 0.87 \[ - \frac{20}{243 \left (3 x + 2\right )^{3}} + \frac{4}{9 \left (3 x + 2\right )^{4}} - \frac{91}{135 \left (3 x + 2\right )^{5}} + \frac{49}{486 \left (3 x + 2\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)/(2+3*x)**7,x)
[Out]
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Mathematica [A] time = 0.0173274, size = 26, normalized size = 0.58 \[ -\frac{5400 x^3+1080 x^2-846 x+311}{2430 (3 x+2)^6} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x))/(2 + 3*x)^7,x]
[Out]
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Maple [A] time = 0.008, size = 38, normalized size = 0.8 \[{\frac{49}{486\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{91}{135\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{4}{9\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{20}{243\, \left ( 2+3\,x \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)/(2+3*x)^7,x)
[Out]
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Maxima [A] time = 1.35069, size = 66, normalized size = 1.47 \[ -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198218, size = 66, normalized size = 1.47 \[ -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.419933, size = 46, normalized size = 1.02 \[ - \frac{5400 x^{3} + 1080 x^{2} - 846 x + 311}{1771470 x^{6} + 7085880 x^{5} + 11809800 x^{4} + 10497600 x^{3} + 5248800 x^{2} + 1399680 x + 155520} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)/(2+3*x)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.206, size = 32, normalized size = 0.71 \[ -\frac{5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \,{\left (3 \, x + 2\right )}^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(2*x - 1)^2/(3*x + 2)^7,x, algorithm="giac")
[Out]