Optimal. Leaf size=105 \[ \frac{10125 (1-2 x)^{19/2}}{2432}-\frac{161325 (1-2 x)^{17/2}}{2176}+\frac{73431}{128} (1-2 x)^{15/2}-\frac{4177401 (1-2 x)^{13/2}}{1664}+\frac{9504551 (1-2 x)^{11/2}}{1408}-\frac{4324397}{384} (1-2 x)^{9/2}+\frac{1405173}{128} (1-2 x)^{7/2}-\frac{3195731}{640} (1-2 x)^{5/2} \]
[Out]
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Rubi [A] time = 0.0743113, 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 \[ \frac{10125 (1-2 x)^{19/2}}{2432}-\frac{161325 (1-2 x)^{17/2}}{2176}+\frac{73431}{128} (1-2 x)^{15/2}-\frac{4177401 (1-2 x)^{13/2}}{1664}+\frac{9504551 (1-2 x)^{11/2}}{1408}-\frac{4324397}{384} (1-2 x)^{9/2}+\frac{1405173}{128} (1-2 x)^{7/2}-\frac{3195731}{640} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 12.1596, size = 94, normalized size = 0.9 \[ \frac{10125 \left (- 2 x + 1\right )^{\frac{19}{2}}}{2432} - \frac{161325 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} + \frac{73431 \left (- 2 x + 1\right )^{\frac{15}{2}}}{128} - \frac{4177401 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} - \frac{4324397 \left (- 2 x + 1\right )^{\frac{9}{2}}}{384} + \frac{1405173 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} - \frac{3195731 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(3/2)*(2+3*x)**4*(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0649255, size = 48, normalized size = 0.46 \[ -\frac{(1-2 x)^{5/2} \left (369208125 x^7+1995171750 x^6+4795033815 x^5+6744559140 x^4+6142984080 x^3+3771434840 x^2+1547888800 x+369438704\right )}{692835} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.006, size = 45, normalized size = 0.4 \[ -{\frac{369208125\,{x}^{7}+1995171750\,{x}^{6}+4795033815\,{x}^{5}+6744559140\,{x}^{4}+6142984080\,{x}^{3}+3771434840\,{x}^{2}+1547888800\,x+369438704}{692835} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34966, size = 99, normalized size = 0.94 \[ \frac{10125}{2432} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} - \frac{161325}{2176} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} + \frac{73431}{128} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} - \frac{4177401}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{9504551}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{4324397}{384} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{1405173}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{3195731}{640} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206876, size = 73, normalized size = 0.7 \[ -\frac{1}{692835} \,{\left (1476832500 \, x^{9} + 6503854500 \, x^{8} + 11568656385 \, x^{7} + 9793273050 \, x^{6} + 2388733575 \, x^{5} - 2741637820 \, x^{4} - 2751200080 \, x^{3} - 942365544 \, x^{2} + 70133984 \, x + 369438704\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4*(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.82992, size = 94, normalized size = 0.9 \[ \frac{10125 \left (- 2 x + 1\right )^{\frac{19}{2}}}{2432} - \frac{161325 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} + \frac{73431 \left (- 2 x + 1\right )^{\frac{15}{2}}}{128} - \frac{4177401 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} - \frac{4324397 \left (- 2 x + 1\right )^{\frac{9}{2}}}{384} + \frac{1405173 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} - \frac{3195731 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(3/2)*(2+3*x)**4*(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.211702, 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)^(3/2),x, algorithm="giac")
[Out]