Optimal. Leaf size=66 \[ -\frac{27}{16} (1-2 x)^{5/2}+\frac{207}{8} (1-2 x)^{3/2}-\frac{1071}{4} \sqrt{1-2 x}-\frac{3283}{8 \sqrt{1-2 x}}+\frac{3773}{48 (1-2 x)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0551939, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{27}{16} (1-2 x)^{5/2}+\frac{207}{8} (1-2 x)^{3/2}-\frac{1071}{4} \sqrt{1-2 x}-\frac{3283}{8 \sqrt{1-2 x}}+\frac{3773}{48 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 7.95968, size = 58, normalized size = 0.88 \[ - \frac{27 \left (- 2 x + 1\right )^{\frac{5}{2}}}{16} + \frac{207 \left (- 2 x + 1\right )^{\frac{3}{2}}}{8} - \frac{1071 \sqrt{- 2 x + 1}}{4} - \frac{3283}{8 \sqrt{- 2 x + 1}} + \frac{3773}{48 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)/(1-2*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0459921, size = 33, normalized size = 0.5 \[ -\frac{81 x^4+459 x^3+2403 x^2-5250 x+1726}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{81\,{x}^{4}+459\,{x}^{3}+2403\,{x}^{2}-5250\,x+1726}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)/(1-2*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.35342, size = 57, normalized size = 0.86 \[ -\frac{27}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{207}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1071}{4} \, \sqrt{-2 \, x + 1} + \frac{49 \,{\left (804 \, x - 325\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222977, size = 49, normalized size = 0.74 \[ \frac{81 \, x^{4} + 459 \, x^{3} + 2403 \, x^{2} - 5250 \, x + 1726}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{3} \left (5 x + 3\right )}{\left (- 2 x + 1\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3*(3+5*x)/(1-2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212248, size = 76, normalized size = 1.15 \[ -\frac{27}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{207}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1071}{4} \, \sqrt{-2 \, x + 1} - \frac{49 \,{\left (804 \, x - 325\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]