Optimal. Leaf size=79 \[ \frac{675}{352} (1-2 x)^{11/2}-\frac{855}{32} (1-2 x)^{9/2}+\frac{17541}{112} (1-2 x)^{7/2}-\frac{39977}{80} (1-2 x)^{5/2}+\frac{91091}{96} (1-2 x)^{3/2}-\frac{41503}{32} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.0702331, antiderivative size = 79, 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 \[ \frac{675}{352} (1-2 x)^{11/2}-\frac{855}{32} (1-2 x)^{9/2}+\frac{17541}{112} (1-2 x)^{7/2}-\frac{39977}{80} (1-2 x)^{5/2}+\frac{91091}{96} (1-2 x)^{3/2}-\frac{41503}{32} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 9.48198, size = 70, normalized size = 0.89 \[ \frac{675 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} - \frac{855 \left (- 2 x + 1\right )^{\frac{9}{2}}}{32} + \frac{17541 \left (- 2 x + 1\right )^{\frac{7}{2}}}{112} - \frac{39977 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} + \frac{91091 \left (- 2 x + 1\right )^{\frac{3}{2}}}{96} - \frac{41503 \sqrt{- 2 x + 1}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)**2/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0489244, size = 38, normalized size = 0.48 \[ -\frac{\sqrt{1-2 x} \left (70875 x^5+316575 x^4+636795 x^3+790023 x^2+743822 x+826982\right )}{1155} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.005, size = 35, normalized size = 0.4 \[ -{\frac{70875\,{x}^{5}+316575\,{x}^{4}+636795\,{x}^{3}+790023\,{x}^{2}+743822\,x+826982}{1155}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)^2/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.36342, size = 74, normalized size = 0.94 \[ \frac{675}{352} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{855}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{17541}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{39977}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{91091}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{41503}{32} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206375, size = 46, normalized size = 0.58 \[ -\frac{1}{1155} \,{\left (70875 \, x^{5} + 316575 \, x^{4} + 636795 \, x^{3} + 790023 \, x^{2} + 743822 \, x + 826982\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.9001, size = 70, normalized size = 0.89 \[ \frac{675 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} - \frac{855 \left (- 2 x + 1\right )^{\frac{9}{2}}}{32} + \frac{17541 \left (- 2 x + 1\right )^{\frac{7}{2}}}{112} - \frac{39977 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} + \frac{91091 \left (- 2 x + 1\right )^{\frac{3}{2}}}{96} - \frac{41503 \sqrt{- 2 x + 1}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3*(3+5*x)**2/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213217, size = 112, normalized size = 1.42 \[ -\frac{675}{352} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{855}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{17541}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{39977}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{91091}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{41503}{32} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="giac")
[Out]