Optimal. Leaf size=92 \[ -\frac{3375}{832} (1-2 x)^{13/2}+\frac{11475}{176} (1-2 x)^{11/2}-\frac{28895}{64} (1-2 x)^{9/2}+\frac{98209}{56} (1-2 x)^{7/2}-\frac{1334949}{320} (1-2 x)^{5/2}+\frac{100793}{16} (1-2 x)^{3/2}-\frac{456533}{64} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.075157, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{3375}{832} (1-2 x)^{13/2}+\frac{11475}{176} (1-2 x)^{11/2}-\frac{28895}{64} (1-2 x)^{9/2}+\frac{98209}{56} (1-2 x)^{7/2}-\frac{1334949}{320} (1-2 x)^{5/2}+\frac{100793}{16} (1-2 x)^{3/2}-\frac{456533}{64} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x)^3)/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 10.5485, size = 82, normalized size = 0.89 \[ - \frac{3375 \left (- 2 x + 1\right )^{\frac{13}{2}}}{832} + \frac{11475 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} - \frac{28895 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{98209 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{1334949 \left (- 2 x + 1\right )^{\frac{5}{2}}}{320} + \frac{100793 \left (- 2 x + 1\right )^{\frac{3}{2}}}{16} - \frac{456533 \sqrt{- 2 x + 1}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)**3/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0517732, size = 43, normalized size = 0.47 \[ -\frac{\sqrt{1-2 x} \left (1299375 x^6+6544125 x^5+14921900 x^4+20766885 x^3+20586249 x^2+17147586 x+18228666\right )}{5005} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x)^3)/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{1299375\,{x}^{6}+6544125\,{x}^{5}+14921900\,{x}^{4}+20766885\,{x}^{3}+20586249\,{x}^{2}+17147586\,x+18228666}{5005}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)^3/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.37141, size = 86, normalized size = 0.93 \[ -\frac{3375}{832} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{11475}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{28895}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{98209}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{1334949}{320} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{100793}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{456533}{64} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.257875, size = 53, normalized size = 0.58 \[ -\frac{1}{5005} \,{\left (1299375 \, x^{6} + 6544125 \, x^{5} + 14921900 \, x^{4} + 20766885 \, x^{3} + 20586249 \, x^{2} + 17147586 \, x + 18228666\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 18.7672, size = 82, normalized size = 0.89 \[ - \frac{3375 \left (- 2 x + 1\right )^{\frac{13}{2}}}{832} + \frac{11475 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} - \frac{28895 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{98209 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{1334949 \left (- 2 x + 1\right )^{\frac{5}{2}}}{320} + \frac{100793 \left (- 2 x + 1\right )^{\frac{3}{2}}}{16} - \frac{456533 \sqrt{- 2 x + 1}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3*(3+5*x)**3/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.233546, size = 134, normalized size = 1.46 \[ -\frac{3375}{832} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{11475}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{28895}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{98209}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{1334949}{320} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{100793}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{456533}{64} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="giac")
[Out]