Optimal. Leaf size=105 \[ \frac{3375}{896} (1-2 x)^{21/2}-\frac{161325 (1-2 x)^{19/2}}{2432}+\frac{1101465 (1-2 x)^{17/2}}{2176}-\frac{1392467}{640} (1-2 x)^{15/2}+\frac{9504551 (1-2 x)^{13/2}}{1664}-\frac{1179381}{128} (1-2 x)^{11/2}+\frac{3278737}{384} (1-2 x)^{9/2}-\frac{456533}{128} (1-2 x)^{7/2} \]
[Out]
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Rubi [A] time = 0.0817825, 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 \[ \frac{3375}{896} (1-2 x)^{21/2}-\frac{161325 (1-2 x)^{19/2}}{2432}+\frac{1101465 (1-2 x)^{17/2}}{2176}-\frac{1392467}{640} (1-2 x)^{15/2}+\frac{9504551 (1-2 x)^{13/2}}{1664}-\frac{1179381}{128} (1-2 x)^{11/2}+\frac{3278737}{384} (1-2 x)^{9/2}-\frac{456533}{128} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(5/2)*(2 + 3*x)^4*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 11.3157, size = 94, normalized size = 0.9 \[ \frac{3375 \left (- 2 x + 1\right )^{\frac{21}{2}}}{896} - \frac{161325 \left (- 2 x + 1\right )^{\frac{19}{2}}}{2432} + \frac{1101465 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} - \frac{1392467 \left (- 2 x + 1\right )^{\frac{15}{2}}}{640} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} - \frac{1179381 \left (- 2 x + 1\right )^{\frac{11}{2}}}{128} + \frac{3278737 \left (- 2 x + 1\right )^{\frac{9}{2}}}{384} - \frac{456533 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(5/2)*(2+3*x)**4*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0638286, size = 48, normalized size = 0.46 \[ -\frac{(1-2 x)^{7/2} \left (212574375 x^7+1127763000 x^6+2642319225 x^5+3583371246 x^4+3089723448 x^3+1740153744 x^2+619493392 x+115708576\right )}{440895} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(5/2)*(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 \[ -{\frac{212574375\,{x}^{7}+1127763000\,{x}^{6}+2642319225\,{x}^{5}+3583371246\,{x}^{4}+3089723448\,{x}^{3}+1740153744\,{x}^{2}+619493392\,x+115708576}{440895} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34387, size = 99, normalized size = 0.94 \[ \frac{3375}{896} \,{\left (-2 \, x + 1\right )}^{\frac{21}{2}} - \frac{161325}{2432} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} + \frac{1101465}{2176} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{1392467}{640} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{9504551}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{1179381}{128} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{3278737}{384} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{456533}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259767, size = 80, normalized size = 0.76 \[ \frac{1}{440895} \,{\left (1700595000 \, x^{10} + 6471211500 \, x^{9} + 8880844050 \, x^{8} + 3513142893 \, x^{7} - 3556515018 \, x^{6} - 4297543173 \, x^{5} - 970928350 \, x^{4} + 842946920 \, x^{3} + 588303696 \, x^{2} + 74758064 \, x - 115708576\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.62769, size = 94, normalized size = 0.9 \[ \frac{3375 \left (- 2 x + 1\right )^{\frac{21}{2}}}{896} - \frac{161325 \left (- 2 x + 1\right )^{\frac{19}{2}}}{2432} + \frac{1101465 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} - \frac{1392467 \left (- 2 x + 1\right )^{\frac{15}{2}}}{640} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} - \frac{1179381 \left (- 2 x + 1\right )^{\frac{11}{2}}}{128} + \frac{3278737 \left (- 2 x + 1\right )^{\frac{9}{2}}}{384} - \frac{456533 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(5/2)*(2+3*x)**4*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.215901, size = 1, normalized size = 0.01 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]