Optimal. Leaf size=66 \[ -\frac{45}{16} (1-2 x)^{5/2}+\frac{85}{2} (1-2 x)^{3/2}-\frac{3467}{8} \sqrt{1-2 x}-\frac{1309}{2 \sqrt{1-2 x}}+\frac{5929}{48 (1-2 x)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0684319, 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 \[ -\frac{45}{16} (1-2 x)^{5/2}+\frac{85}{2} (1-2 x)^{3/2}-\frac{3467}{8} \sqrt{1-2 x}-\frac{1309}{2 \sqrt{1-2 x}}+\frac{5929}{48 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 8.44317, size = 58, normalized size = 0.88 \[ - \frac{45 \left (- 2 x + 1\right )^{\frac{5}{2}}}{16} + \frac{85 \left (- 2 x + 1\right )^{\frac{3}{2}}}{2} - \frac{3467 \sqrt{- 2 x + 1}}{8} - \frac{1309}{2 \sqrt{- 2 x + 1}} + \frac{5929}{48 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2*(3+5*x)**2/(1-2*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0497516, size = 33, normalized size = 0.5 \[ -\frac{135 x^4+750 x^3+3873 x^2-8430 x+2774}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^2*(3 + 5*x)^2)/(1 - 2*x)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{135\,{x}^{4}+750\,{x}^{3}+3873\,{x}^{2}-8430\,x+2774}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2*(3+5*x)^2/(1-2*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.33777, size = 57, normalized size = 0.86 \[ -\frac{45}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{85}{2} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3467}{8} \, \sqrt{-2 \, x + 1} + \frac{77 \,{\left (816 \, x - 331\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20808, size = 49, normalized size = 0.74 \[ \frac{135 \, x^{4} + 750 \, x^{3} + 3873 \, x^{2} - 8430 \, x + 2774}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{2} \left (5 x + 3\right )^{2}}{\left (- 2 x + 1\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2*(3+5*x)**2/(1-2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212353, size = 76, normalized size = 1.15 \[ -\frac{45}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{85}{2} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3467}{8} \, \sqrt{-2 \, x + 1} - \frac{77 \,{\left (816 \, x - 331\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^2/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]