Optimal. Leaf size=79 \[ \frac{405}{352} (1-2 x)^{11/2}-\frac{519}{32} (1-2 x)^{9/2}+\frac{1539}{16} (1-2 x)^{7/2}-\frac{24843}{80} (1-2 x)^{5/2}+\frac{57281}{96} (1-2 x)^{3/2}-\frac{26411}{32} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.0623013, antiderivative size = 79, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{405}{352} (1-2 x)^{11/2}-\frac{519}{32} (1-2 x)^{9/2}+\frac{1539}{16} (1-2 x)^{7/2}-\frac{24843}{80} (1-2 x)^{5/2}+\frac{57281}{96} (1-2 x)^{3/2}-\frac{26411}{32} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^4*(3 + 5*x))/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 8.72704, size = 70, normalized size = 0.89 \[ \frac{405 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} - \frac{519 \left (- 2 x + 1\right )^{\frac{9}{2}}}{32} + \frac{1539 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} - \frac{24843 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} + \frac{57281 \left (- 2 x + 1\right )^{\frac{3}{2}}}{96} - \frac{26411 \sqrt{- 2 x + 1}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0244733, size = 38, normalized size = 0.48 \[ -\frac{1}{165} \sqrt{1-2 x} \left (6075 x^5+27630 x^4+56520 x^3+71136 x^2+67664 x+75584\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^4*(3 + 5*x))/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.005, size = 35, normalized size = 0.4 \[ -{\frac{6075\,{x}^{5}+27630\,{x}^{4}+56520\,{x}^{3}+71136\,{x}^{2}+67664\,x+75584}{165}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.34961, size = 74, normalized size = 0.94 \[ \frac{405}{352} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{519}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{1539}{16} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{24843}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{57281}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{26411}{32} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204675, size = 46, normalized size = 0.58 \[ -\frac{1}{165} \,{\left (6075 \, x^{5} + 27630 \, x^{4} + 56520 \, x^{3} + 71136 \, x^{2} + 67664 \, x + 75584\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.9001, size = 70, normalized size = 0.89 \[ \frac{405 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} - \frac{519 \left (- 2 x + 1\right )^{\frac{9}{2}}}{32} + \frac{1539 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} - \frac{24843 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} + \frac{57281 \left (- 2 x + 1\right )^{\frac{3}{2}}}{96} - \frac{26411 \sqrt{- 2 x + 1}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**4*(3+5*x)/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.209187, size = 112, normalized size = 1.42 \[ -\frac{405}{352} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{519}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{1539}{16} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{24843}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{57281}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{26411}{32} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4/sqrt(-2*x + 1),x, algorithm="giac")
[Out]