Optimal. Leaf size=79 \[ \frac{1125}{352} (1-2 x)^{11/2}-\frac{4225}{96} (1-2 x)^{9/2}+\frac{28555}{112} (1-2 x)^{7/2}-\frac{64317}{80} (1-2 x)^{5/2}+\frac{48279}{32} (1-2 x)^{3/2}-\frac{65219}{32} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.0707825, 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 \[ \frac{1125}{352} (1-2 x)^{11/2}-\frac{4225}{96} (1-2 x)^{9/2}+\frac{28555}{112} (1-2 x)^{7/2}-\frac{64317}{80} (1-2 x)^{5/2}+\frac{48279}{32} (1-2 x)^{3/2}-\frac{65219}{32} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^2*(3 + 5*x)^3)/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 9.55476, size = 70, normalized size = 0.89 \[ \frac{1125 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} - \frac{4225 \left (- 2 x + 1\right )^{\frac{9}{2}}}{96} + \frac{28555 \left (- 2 x + 1\right )^{\frac{7}{2}}}{112} - \frac{64317 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} + \frac{48279 \left (- 2 x + 1\right )^{\frac{3}{2}}}{32} - \frac{65219 \sqrt{- 2 x + 1}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2*(3+5*x)**3/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0481702, size = 38, normalized size = 0.48 \[ -\frac{\sqrt{1-2 x} \left (118125 x^5+518000 x^4+1024475 x^3+1252938 x^2+1167932 x+1292672\right )}{1155} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^2*(3 + 5*x)^3)/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.007, size = 35, normalized size = 0.4 \[ -{\frac{118125\,{x}^{5}+518000\,{x}^{4}+1024475\,{x}^{3}+1252938\,{x}^{2}+1167932\,x+1292672}{1155}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2*(3+5*x)^3/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.33305, size = 74, normalized size = 0.94 \[ \frac{1125}{352} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{4225}{96} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{28555}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{64317}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{48279}{32} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{65219}{32} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^2/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234502, size = 46, normalized size = 0.58 \[ -\frac{1}{1155} \,{\left (118125 \, x^{5} + 518000 \, x^{4} + 1024475 \, x^{3} + 1252938 \, x^{2} + 1167932 \, x + 1292672\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^2/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.7588, size = 70, normalized size = 0.89 \[ \frac{1125 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} - \frac{4225 \left (- 2 x + 1\right )^{\frac{9}{2}}}{96} + \frac{28555 \left (- 2 x + 1\right )^{\frac{7}{2}}}{112} - \frac{64317 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} + \frac{48279 \left (- 2 x + 1\right )^{\frac{3}{2}}}{32} - \frac{65219 \sqrt{- 2 x + 1}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2*(3+5*x)**3/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.228861, size = 112, normalized size = 1.42 \[ -\frac{1125}{352} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{4225}{96} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{28555}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{64317}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{48279}{32} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{65219}{32} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^2/sqrt(-2*x + 1),x, algorithm="giac")
[Out]