Optimal. Leaf size=66 \[ -\frac{25}{16} (1-2 x)^{9/2}+\frac{255}{14} (1-2 x)^{7/2}-\frac{3467}{40} (1-2 x)^{5/2}+\frac{1309}{6} (1-2 x)^{3/2}-\frac{5929}{16} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.0639656, antiderivative size = 66, 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 \[ -\frac{25}{16} (1-2 x)^{9/2}+\frac{255}{14} (1-2 x)^{7/2}-\frac{3467}{40} (1-2 x)^{5/2}+\frac{1309}{6} (1-2 x)^{3/2}-\frac{5929}{16} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^2*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 8.39035, size = 58, normalized size = 0.88 \[ - \frac{25 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} + \frac{255 \left (- 2 x + 1\right )^{\frac{7}{2}}}{14} - \frac{3467 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} + \frac{1309 \left (- 2 x + 1\right )^{\frac{3}{2}}}{6} - \frac{5929 \sqrt{- 2 x + 1}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2*(3+5*x)**2/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0457333, size = 33, normalized size = 0.5 \[ -\frac{1}{105} \sqrt{1-2 x} \left (2625 x^4+10050 x^3+17391 x^2+19574 x+23354\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^2*(3 + 5*x)^2)/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{2625\,{x}^{4}+10050\,{x}^{3}+17391\,{x}^{2}+19574\,x+23354}{105}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2*(3+5*x)^2/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.34345, size = 62, normalized size = 0.94 \[ -\frac{25}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{255}{14} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{3467}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{1309}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{5929}{16} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201366, size = 39, normalized size = 0.59 \[ -\frac{1}{105} \,{\left (2625 \, x^{4} + 10050 \, x^{3} + 17391 \, x^{2} + 19574 \, x + 23354\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.88765, size = 58, normalized size = 0.88 \[ - \frac{25 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} + \frac{255 \left (- 2 x + 1\right )^{\frac{7}{2}}}{14} - \frac{3467 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} + \frac{1309 \left (- 2 x + 1\right )^{\frac{3}{2}}}{6} - \frac{5929 \sqrt{- 2 x + 1}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2*(3+5*x)**2/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211166, size = 90, normalized size = 1.36 \[ -\frac{25}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{255}{14} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{3467}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{1309}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{5929}{16} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/sqrt(-2*x + 1),x, algorithm="giac")
[Out]