Optimal. Leaf size=118 \[ -\frac{30375 (1-2 x)^{13/2}}{3328}+\frac{277425 (1-2 x)^{11/2}}{1408}-\frac{246315}{128} (1-2 x)^{9/2}+\frac{10121229}{896} (1-2 x)^{7/2}-\frac{2887773}{64} (1-2 x)^{5/2}+\frac{52725715}{384} (1-2 x)^{3/2}-\frac{60160485}{128} \sqrt{1-2 x}-\frac{39220335}{128 \sqrt{1-2 x}}+\frac{22370117}{768 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0914841, antiderivative size = 118, 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 \[ -\frac{30375 (1-2 x)^{13/2}}{3328}+\frac{277425 (1-2 x)^{11/2}}{1408}-\frac{246315}{128} (1-2 x)^{9/2}+\frac{10121229}{896} (1-2 x)^{7/2}-\frac{2887773}{64} (1-2 x)^{5/2}+\frac{52725715}{384} (1-2 x)^{3/2}-\frac{60160485}{128} \sqrt{1-2 x}-\frac{39220335}{128 \sqrt{1-2 x}}+\frac{22370117}{768 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 12.398, size = 105, normalized size = 0.89 \[ - \frac{30375 \left (- 2 x + 1\right )^{\frac{13}{2}}}{3328} + \frac{277425 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} - \frac{246315 \left (- 2 x + 1\right )^{\frac{9}{2}}}{128} + \frac{10121229 \left (- 2 x + 1\right )^{\frac{7}{2}}}{896} - \frac{2887773 \left (- 2 x + 1\right )^{\frac{5}{2}}}{64} + \frac{52725715 \left (- 2 x + 1\right )^{\frac{3}{2}}}{384} - \frac{60160485 \sqrt{- 2 x + 1}}{128} - \frac{39220335}{128 \sqrt{- 2 x + 1}} + \frac{22370117}{768 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**5*(3+5*x)**3/(1-2*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0659168, size = 53, normalized size = 0.45 \[ -\frac{7016625 x^8+47670525 x^7+153878760 x^6+324478899 x^5+540496701 x^4+905206628 x^3+2892917004 x^2-5818266408 x+1938557272}{3003 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^5*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 50, normalized size = 0.4 \[ -{\frac{7016625\,{x}^{8}+47670525\,{x}^{7}+153878760\,{x}^{6}+324478899\,{x}^{5}+540496701\,{x}^{4}+905206628\,{x}^{3}+2892917004\,{x}^{2}-5818266408\,x+1938557272}{3003} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^5*(3+5*x)^3/(1-2*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.33201, size = 105, normalized size = 0.89 \[ -\frac{30375}{3328} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{277425}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{246315}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{10121229}{896} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{2887773}{64} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{52725715}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{60160485}{128} \, \sqrt{-2 \, x + 1} + \frac{290521 \,{\left (1620 \, x - 733\right )}}{768 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211623, size = 76, normalized size = 0.64 \[ \frac{7016625 \, x^{8} + 47670525 \, x^{7} + 153878760 \, x^{6} + 324478899 \, x^{5} + 540496701 \, x^{4} + 905206628 \, x^{3} + 2892917004 \, x^{2} - 5818266408 \, x + 1938557272}{3003 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{5} \left (5 x + 3\right )^{3}}{\left (- 2 x + 1\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**5*(3+5*x)**3/(1-2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216024, size = 162, normalized size = 1.37 \[ -\frac{30375}{3328} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{277425}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{246315}{128} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{10121229}{896} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{2887773}{64} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{52725715}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{60160485}{128} \, \sqrt{-2 \, x + 1} - \frac{290521 \,{\left (1620 \, x - 733\right )}}{768 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)^5/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]