Optimal. Leaf size=40 \[ -\frac{5}{12} (1-2 x)^{9/2}+\frac{17}{7} (1-2 x)^{7/2}-\frac{77}{20} (1-2 x)^{5/2} \]
[Out]
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Rubi [A] time = 0.0344212, antiderivative size = 40, 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 \[ -\frac{5}{12} (1-2 x)^{9/2}+\frac{17}{7} (1-2 x)^{7/2}-\frac{77}{20} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x),x]
[Out]
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Rubi in Sympy [A] time = 6.06836, size = 34, normalized size = 0.85 \[ - \frac{5 \left (- 2 x + 1\right )^{\frac{9}{2}}}{12} + \frac{17 \left (- 2 x + 1\right )^{\frac{7}{2}}}{7} - \frac{77 \left (- 2 x + 1\right )^{\frac{5}{2}}}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(3/2)*(2+3*x)*(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0138271, size = 23, normalized size = 0.57 \[ -\frac{1}{105} (1-2 x)^{5/2} \left (175 x^2+335 x+193\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)*(3 + 5*x),x]
[Out]
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Maple [A] time = 0.003, size = 20, normalized size = 0.5 \[ -{\frac{175\,{x}^{2}+335\,x+193}{105} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(3/2)*(2+3*x)*(3+5*x),x)
[Out]
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Maxima [A] time = 1.35584, size = 38, normalized size = 0.95 \[ -\frac{5}{12} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{17}{7} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{77}{20} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)*(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224346, size = 39, normalized size = 0.98 \[ -\frac{1}{105} \,{\left (700 \, x^{4} + 640 \, x^{3} - 393 \, x^{2} - 437 \, x + 193\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)*(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.79387, size = 34, normalized size = 0.85 \[ - \frac{5 \left (- 2 x + 1\right )^{\frac{9}{2}}}{12} + \frac{17 \left (- 2 x + 1\right )^{\frac{7}{2}}}{7} - \frac{77 \left (- 2 x + 1\right )^{\frac{5}{2}}}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(3/2)*(2+3*x)*(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.237516, size = 66, normalized size = 1.65 \[ -\frac{5}{12} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{17}{7} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{77}{20} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)*(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]