Optimal. Leaf size=66 \[ -\frac{225}{112} (1-2 x)^{7/2}+\frac{51}{2} (1-2 x)^{5/2}-\frac{3467}{24} (1-2 x)^{3/2}+\frac{1309}{2} \sqrt{1-2 x}+\frac{5929}{16 \sqrt{1-2 x}} \]
[Out]
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Rubi [A] time = 0.0619145, 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 \[ -\frac{225}{112} (1-2 x)^{7/2}+\frac{51}{2} (1-2 x)^{5/2}-\frac{3467}{24} (1-2 x)^{3/2}+\frac{1309}{2} \sqrt{1-2 x}+\frac{5929}{16 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 8.84576, size = 58, normalized size = 0.88 \[ - \frac{225 \left (- 2 x + 1\right )^{\frac{7}{2}}}{112} + \frac{51 \left (- 2 x + 1\right )^{\frac{5}{2}}}{2} - \frac{3467 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} + \frac{1309 \sqrt{- 2 x + 1}}{2} + \frac{5929}{16 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2*(3+5*x)**2/(1-2*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0502549, size = 33, normalized size = 0.5 \[ \frac{-675 x^4-2934 x^3-6721 x^2-18230 x+18986}{21 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{675\,{x}^{4}+2934\,{x}^{3}+6721\,{x}^{2}+18230\,x-18986}{21}{\frac{1}{\sqrt{1-2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2*(3+5*x)^2/(1-2*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.34079, size = 62, normalized size = 0.94 \[ -\frac{225}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{51}{2} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{3467}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1309}{2} \, \sqrt{-2 \, x + 1} + \frac{5929}{16 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216797, size = 39, normalized size = 0.59 \[ -\frac{675 \, x^{4} + 2934 \, x^{3} + 6721 \, x^{2} + 18230 \, x - 18986}{21 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{2} \left (5 x + 3\right )^{2}}{\left (- 2 x + 1\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2*(3+5*x)**2/(1-2*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216828, size = 81, normalized size = 1.23 \[ \frac{225}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{51}{2} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{3467}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1309}{2} \, \sqrt{-2 \, x + 1} + \frac{5929}{16 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]