Optimal. Leaf size=56 \[ -\frac{250 (3 x+2)^{13}}{3159}+\frac{1025 (3 x+2)^{12}}{2916}-\frac{185}{891} (3 x+2)^{11}+\frac{107 (3 x+2)^{10}}{2430}-\frac{7 (3 x+2)^9}{2187} \]
[Out]
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Rubi [A] time = 0.0927637, antiderivative size = 56, 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 \[ -\frac{250 (3 x+2)^{13}}{3159}+\frac{1025 (3 x+2)^{12}}{2916}-\frac{185}{891} (3 x+2)^{11}+\frac{107 (3 x+2)^{10}}{2430}-\frac{7 (3 x+2)^9}{2187} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 14.0084, size = 49, normalized size = 0.88 \[ - \frac{250 \left (3 x + 2\right )^{13}}{3159} + \frac{1025 \left (3 x + 2\right )^{12}}{2916} - \frac{185 \left (3 x + 2\right )^{11}}{891} + \frac{107 \left (3 x + 2\right )^{10}}{2430} - \frac{7 \left (3 x + 2\right )^{9}}{2187} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)**8*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.00358125, size = 74, normalized size = 1.32 \[ -\frac{1640250 x^{13}}{13}-\frac{3626775 x^{12}}{4}-\frac{32079645 x^{11}}{11}-\frac{54794799 x^{10}}{10}-6524829 x^9-4865076 x^8-1830960 x^7+350128 x^6+\frac{4580384 x^5}{5}+597824 x^4+224256 x^3+51840 x^2+6912 x \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)*(2 + 3*x)^8*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.003, size = 65, normalized size = 1.2 \[ -{\frac{1640250\,{x}^{13}}{13}}-{\frac{3626775\,{x}^{12}}{4}}-{\frac{32079645\,{x}^{11}}{11}}-{\frac{54794799\,{x}^{10}}{10}}-6524829\,{x}^{9}-4865076\,{x}^{8}-1830960\,{x}^{7}+350128\,{x}^{6}+{\frac{4580384\,{x}^{5}}{5}}+597824\,{x}^{4}+224256\,{x}^{3}+51840\,{x}^{2}+6912\,x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)^8*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34306, size = 86, normalized size = 1.54 \[ -\frac{1640250}{13} \, x^{13} - \frac{3626775}{4} \, x^{12} - \frac{32079645}{11} \, x^{11} - \frac{54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac{4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^8*(2*x - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.186057, size = 1, normalized size = 0.02 \[ -\frac{1640250}{13} x^{13} - \frac{3626775}{4} x^{12} - \frac{32079645}{11} x^{11} - \frac{54794799}{10} x^{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac{4580384}{5} x^{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^8*(2*x - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.120772, size = 71, normalized size = 1.27 \[ - \frac{1640250 x^{13}}{13} - \frac{3626775 x^{12}}{4} - \frac{32079645 x^{11}}{11} - \frac{54794799 x^{10}}{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac{4580384 x^{5}}{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)**8*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206994, size = 86, normalized size = 1.54 \[ -\frac{1640250}{13} \, x^{13} - \frac{3626775}{4} \, x^{12} - \frac{32079645}{11} \, x^{11} - \frac{54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac{4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^3*(3*x + 2)^8*(2*x - 1),x, algorithm="giac")
[Out]