Optimal. Leaf size=92 \[ -\frac{3375 (1-2 x)^{17/2}}{1088}+\frac{765}{16} (1-2 x)^{15/2}-\frac{260055}{832} (1-2 x)^{13/2}+\frac{98209}{88} (1-2 x)^{11/2}-\frac{444983}{192} (1-2 x)^{9/2}+\frac{43197}{16} (1-2 x)^{7/2}-\frac{456533}{320} (1-2 x)^{5/2} \]
[Out]
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Rubi [A] time = 0.0687739, 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 \[ -\frac{3375 (1-2 x)^{17/2}}{1088}+\frac{765}{16} (1-2 x)^{15/2}-\frac{260055}{832} (1-2 x)^{13/2}+\frac{98209}{88} (1-2 x)^{11/2}-\frac{444983}{192} (1-2 x)^{9/2}+\frac{43197}{16} (1-2 x)^{7/2}-\frac{456533}{320} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 10.9318, size = 82, normalized size = 0.89 \[ - \frac{3375 \left (- 2 x + 1\right )^{\frac{17}{2}}}{1088} + \frac{765 \left (- 2 x + 1\right )^{\frac{15}{2}}}{16} - \frac{260055 \left (- 2 x + 1\right )^{\frac{13}{2}}}{832} + \frac{98209 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} - \frac{444983 \left (- 2 x + 1\right )^{\frac{9}{2}}}{192} + \frac{43197 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} - \frac{456533 \left (- 2 x + 1\right )^{\frac{5}{2}}}{320} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(3/2)*(2+3*x)**3*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0567208, size = 43, normalized size = 0.47 \[ -\frac{(1-2 x)^{5/2} \left (7239375 x^6+34073325 x^5+70032600 x^4+82215885 x^3+60296725 x^2+27917090 x+7158706\right )}{36465} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{7239375\,{x}^{6}+34073325\,{x}^{5}+70032600\,{x}^{4}+82215885\,{x}^{3}+60296725\,{x}^{2}+27917090\,x+7158706}{36465} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35957, size = 86, normalized size = 0.93 \[ -\frac{3375}{1088} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} + \frac{765}{16} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} - \frac{260055}{832} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{98209}{88} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{444983}{192} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{43197}{16} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{456533}{320} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^3*(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204799, size = 66, normalized size = 0.72 \[ -\frac{1}{36465} \,{\left (28957500 \, x^{8} + 107335800 \, x^{7} + 151076475 \, x^{6} + 82806465 \, x^{5} - 17644040 \, x^{4} - 47302655 \, x^{3} - 22736811 \, x^{2} - 717734 \, x + 7158706\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^3*(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.17803, size = 82, normalized size = 0.89 \[ - \frac{3375 \left (- 2 x + 1\right )^{\frac{17}{2}}}{1088} + \frac{765 \left (- 2 x + 1\right )^{\frac{15}{2}}}{16} - \frac{260055 \left (- 2 x + 1\right )^{\frac{13}{2}}}{832} + \frac{98209 \left (- 2 x + 1\right )^{\frac{11}{2}}}{88} - \frac{444983 \left (- 2 x + 1\right )^{\frac{9}{2}}}{192} + \frac{43197 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} - \frac{456533 \left (- 2 x + 1\right )^{\frac{5}{2}}}{320} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(3/2)*(2+3*x)**3*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.213685, size = 153, normalized size = 1.66 \[ -\frac{3375}{1088} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} - \frac{765}{16} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} - \frac{260055}{832} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{98209}{88} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{444983}{192} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{43197}{16} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{456533}{320} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^3*(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]