Optimal. Leaf size=105 \[ \frac{10125 (1-2 x)^{11/2}}{1408}-\frac{17925}{128} (1-2 x)^{9/2}+\frac{1101465}{896} (1-2 x)^{7/2}-\frac{4177401}{640} (1-2 x)^{5/2}+\frac{9504551}{384} (1-2 x)^{3/2}-\frac{12973191}{128} \sqrt{1-2 x}-\frac{9836211}{128 \sqrt{1-2 x}}+\frac{3195731}{384 (1-2 x)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0857993, antiderivative size = 105, 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 \[ \frac{10125 (1-2 x)^{11/2}}{1408}-\frac{17925}{128} (1-2 x)^{9/2}+\frac{1101465}{896} (1-2 x)^{7/2}-\frac{4177401}{640} (1-2 x)^{5/2}+\frac{9504551}{384} (1-2 x)^{3/2}-\frac{12973191}{128} \sqrt{1-2 x}-\frac{9836211}{128 \sqrt{1-2 x}}+\frac{3195731}{384 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 11.3437, size = 94, normalized size = 0.9 \[ \frac{10125 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} - \frac{17925 \left (- 2 x + 1\right )^{\frac{9}{2}}}{128} + \frac{1101465 \left (- 2 x + 1\right )^{\frac{7}{2}}}{896} - \frac{4177401 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} + \frac{9504551 \left (- 2 x + 1\right )^{\frac{3}{2}}}{384} - \frac{12973191 \sqrt{- 2 x + 1}}{128} - \frac{9836211}{128 \sqrt{- 2 x + 1}} + \frac{3195731}{384 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)**3/(1-2*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0611024, size = 48, normalized size = 0.46 \[ -\frac{1063125 x^7+6630750 x^6+19961775 x^5+41201532 x^4+77493296 x^3+258342648 x^2-522173856 x+173891632}{1155 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^4*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 45, normalized size = 0.4 \[ -{\frac{1063125\,{x}^{7}+6630750\,{x}^{6}+19961775\,{x}^{5}+41201532\,{x}^{4}+77493296\,{x}^{3}+258342648\,{x}^{2}-522173856\,x+173891632}{1155} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)^3/(1-2*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.32226, size = 93, normalized size = 0.89 \[ \frac{10125}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{17925}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{1101465}{896} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{4177401}{640} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{9504551}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{12973191}{128} \, \sqrt{-2 \, x + 1} + \frac{41503 \,{\left (711 \, x - 317\right )}}{192 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211545, size = 69, normalized size = 0.66 \[ \frac{1063125 \, x^{7} + 6630750 \, x^{6} + 19961775 \, x^{5} + 41201532 \, x^{4} + 77493296 \, x^{3} + 258342648 \, x^{2} - 522173856 \, x + 173891632}{1155 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{4} \left (5 x + 3\right )^{3}}{\left (- 2 x + 1\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**4*(3+5*x)**3/(1-2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.248106, size = 140, normalized size = 1.33 \[ -\frac{10125}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{17925}{128} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{1101465}{896} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{4177401}{640} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{9504551}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{12973191}{128} \, \sqrt{-2 \, x + 1} - \frac{41503 \,{\left (711 \, x - 317\right )}}{192 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]