Optimal. Leaf size=105 \[ \frac{10125 (1-2 x)^{17/2}}{2176}-\frac{10755}{128} (1-2 x)^{15/2}+\frac{1101465 (1-2 x)^{13/2}}{1664}-\frac{4177401 (1-2 x)^{11/2}}{1408}+\frac{9504551 (1-2 x)^{9/2}}{1152}-\frac{1853313}{128} (1-2 x)^{7/2}+\frac{9836211}{640} (1-2 x)^{5/2}-\frac{3195731}{384} (1-2 x)^{3/2} \]
[Out]
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Rubi [A] time = 0.0746184, antiderivative size = 105, 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 \[ \frac{10125 (1-2 x)^{17/2}}{2176}-\frac{10755}{128} (1-2 x)^{15/2}+\frac{1101465 (1-2 x)^{13/2}}{1664}-\frac{4177401 (1-2 x)^{11/2}}{1408}+\frac{9504551 (1-2 x)^{9/2}}{1152}-\frac{1853313}{128} (1-2 x)^{7/2}+\frac{9836211}{640} (1-2 x)^{5/2}-\frac{3195731}{384} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 11.2985, size = 94, normalized size = 0.9 \[ \frac{10125 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} - \frac{10755 \left (- 2 x + 1\right )^{\frac{15}{2}}}{128} + \frac{1101465 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} - \frac{4177401 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{9}{2}}}{1152} - \frac{1853313 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} + \frac{9836211 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} - \frac{3195731 \left (- 2 x + 1\right )^{\frac{3}{2}}}{384} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)**3*(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0624309, size = 48, normalized size = 0.46 \[ -\frac{(1-2 x)^{3/2} \left (65154375 x^7+360231300 x^6+894452625 x^5+1320982290 x^4+1299289000 x^3+906777120 x^2+466679856 x+171312832\right )}{109395} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.007, size = 45, normalized size = 0.4 \[ -{\frac{65154375\,{x}^{7}+360231300\,{x}^{6}+894452625\,{x}^{5}+1320982290\,{x}^{4}+1299289000\,{x}^{3}+906777120\,{x}^{2}+466679856\,x+171312832}{109395} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)^3*(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.33893, size = 99, normalized size = 0.94 \[ \frac{10125}{2176} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{10755}{128} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{1101465}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{4177401}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{9504551}{1152} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{1853313}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{9836211}{640} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{3195731}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207347, size = 66, normalized size = 0.63 \[ \frac{1}{109395} \,{\left (130308750 \, x^{8} + 655308225 \, x^{7} + 1428673950 \, x^{6} + 1747511955 \, x^{5} + 1277595710 \, x^{4} + 514265240 \, x^{3} + 26582592 \, x^{2} - 124054192 \, x - 171312832\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.69919, size = 94, normalized size = 0.9 \[ \frac{10125 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} - \frac{10755 \left (- 2 x + 1\right )^{\frac{15}{2}}}{128} + \frac{1101465 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} - \frac{4177401 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{9}{2}}}{1152} - \frac{1853313 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} + \frac{9836211 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} - \frac{3195731 \left (- 2 x + 1\right )^{\frac{3}{2}}}{384} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**4*(3+5*x)**3*(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216035, size = 165, normalized size = 1.57 \[ \frac{10125}{2176} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{10755}{128} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{1101465}{1664} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{4177401}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{9504551}{1152} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{1853313}{128} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{9836211}{640} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{3195731}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="giac")
[Out]