Optimal. Leaf size=67 \[ \frac{500 (3 x+2)^{11}}{8019}-\frac{380}{729} (3 x+2)^{10}+\frac{8285 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{5832}+\frac{109}{729} (3 x+2)^7-\frac{49 (3 x+2)^6}{4374} \]
[Out]
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Rubi [A] time = 0.100915, antiderivative size = 67, 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 \[ \frac{500 (3 x+2)^{11}}{8019}-\frac{380}{729} (3 x+2)^{10}+\frac{8285 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{5832}+\frac{109}{729} (3 x+2)^7-\frac{49 (3 x+2)^6}{4374} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{121500 x^{11}}{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349 x^{8}}{8} - 987 x^{7} - \frac{252329 x^{6}}{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 864 x + 7344 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**5*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00401323, size = 60, normalized size = 0.9 \[ \frac{121500 x^{11}}{11}+50220 x^{10}+89655 x^9+\frac{551349 x^8}{8}-987 x^7-\frac{252329 x^6}{6}-28322 x^5-2150 x^4+6432 x^3+3672 x^2+864 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.003, size = 55, normalized size = 0.8 \[{\frac{121500\,{x}^{11}}{11}}+50220\,{x}^{10}+89655\,{x}^{9}+{\frac{551349\,{x}^{8}}{8}}-987\,{x}^{7}-{\frac{252329\,{x}^{6}}{6}}-28322\,{x}^{5}-2150\,{x}^{4}+6432\,{x}^{3}+3672\,{x}^{2}+864\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^5*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34708, size = 73, normalized size = 1.09 \[ \frac{121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac{551349}{8} \, x^{8} - 987 \, x^{7} - \frac{252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5*(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.180019, size = 1, normalized size = 0.01 \[ \frac{121500}{11} x^{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349}{8} x^{8} - 987 x^{7} - \frac{252329}{6} x^{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5*(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.118182, size = 58, normalized size = 0.87 \[ \frac{121500 x^{11}}{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349 x^{8}}{8} - 987 x^{7} - \frac{252329 x^{6}}{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**5*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.218336, size = 73, normalized size = 1.09 \[ \frac{121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac{551349}{8} \, x^{8} - 987 \, x^{7} - \frac{252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5*(2*x - 1)^2,x, algorithm="giac")
[Out]