Optimal. Leaf size=66 \[ -\frac{135}{112} (1-2 x)^{7/2}+\frac{621}{40} (1-2 x)^{5/2}-\frac{357}{4} (1-2 x)^{3/2}+\frac{3283}{8} \sqrt{1-2 x}+\frac{3773}{16 \sqrt{1-2 x}} \]
[Out]
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Rubi [A] time = 0.0590695, 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 \[ -\frac{135}{112} (1-2 x)^{7/2}+\frac{621}{40} (1-2 x)^{5/2}-\frac{357}{4} (1-2 x)^{3/2}+\frac{3283}{8} \sqrt{1-2 x}+\frac{3773}{16 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 8.20089, size = 58, normalized size = 0.88 \[ - \frac{135 \left (- 2 x + 1\right )^{\frac{7}{2}}}{112} + \frac{621 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} - \frac{357 \left (- 2 x + 1\right )^{\frac{3}{2}}}{4} + \frac{3283 \sqrt{- 2 x + 1}}{8} + \frac{3773}{16 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)/(1-2*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.038557, size = 37, normalized size = 0.56 \[ \frac{\sqrt{1-2 x} \left (675 x^4+2997 x^3+6987 x^2+19154 x-19994\right )}{70 x-35} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x))/(1 - 2*x)^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 30, normalized size = 0.5 \[ -{\frac{675\,{x}^{4}+2997\,{x}^{3}+6987\,{x}^{2}+19154\,x-19994}{35}{\frac{1}{\sqrt{1-2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)/(1-2*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.3357, size = 62, normalized size = 0.94 \[ -\frac{135}{112} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{621}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{357}{4} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{3283}{8} \, \sqrt{-2 \, x + 1} + \frac{3773}{16 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211663, size = 39, normalized size = 0.59 \[ -\frac{675 \, x^{4} + 2997 \, x^{3} + 6987 \, x^{2} + 19154 \, x - 19994}{35 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{3} \left (5 x + 3\right )}{\left (- 2 x + 1\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3*(3+5*x)/(1-2*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.210035, size = 81, normalized size = 1.23 \[ \frac{135}{112} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{621}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{357}{4} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{3283}{8} \, \sqrt{-2 \, x + 1} + \frac{3773}{16 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]