Optimal. Leaf size=86 \[ -\frac{1612242}{2401 (3 x+2)}-\frac{3125}{11 (5 x+3)}-\frac{34371}{686 (3 x+2)^2}-\frac{216}{49 (3 x+2)^3}-\frac{9}{28 (3 x+2)^4}-\frac{64 \log (1-2 x)}{2033647}+\frac{70752609 \log (3 x+2)}{16807}-\frac{509375}{121} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0955364, antiderivative size = 86, 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 \[ -\frac{1612242}{2401 (3 x+2)}-\frac{3125}{11 (5 x+3)}-\frac{34371}{686 (3 x+2)^2}-\frac{216}{49 (3 x+2)^3}-\frac{9}{28 (3 x+2)^4}-\frac{64 \log (1-2 x)}{2033647}+\frac{70752609 \log (3 x+2)}{16807}-\frac{509375}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 12.7336, size = 73, normalized size = 0.85 \[ - \frac{64 \log{\left (- 2 x + 1 \right )}}{2033647} + \frac{70752609 \log{\left (3 x + 2 \right )}}{16807} - \frac{509375 \log{\left (5 x + 3 \right )}}{121} - \frac{3125}{11 \left (5 x + 3\right )} - \frac{1612242}{2401 \left (3 x + 2\right )} - \frac{34371}{686 \left (3 x + 2\right )^{2}} - \frac{216}{49 \left (3 x + 2\right )^{3}} - \frac{9}{28 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**5/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0559289, size = 84, normalized size = 0.98 \[ -\frac{1612242}{2401 (3 x+2)}-\frac{3125}{55 x+33}-\frac{34371}{686 (3 x+2)^2}-\frac{216}{49 (3 x+2)^3}-\frac{9}{28 (3 x+2)^4}-\frac{64 \log (1-2 x)}{2033647}+\frac{70752609 \log (6 x+4)}{16807}-\frac{509375}{121} \log (10 x+6) \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.016, size = 71, normalized size = 0.8 \[ -{\frac{3125}{33+55\,x}}-{\frac{509375\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{9}{28\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{216}{49\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{34371}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{1612242}{4802+7203\,x}}+{\frac{70752609\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{64\,\ln \left ( -1+2\,x \right ) }{2033647}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^5/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.32919, size = 100, normalized size = 1.16 \[ -\frac{12007729980 \, x^{4} + 31620356478 \, x^{3} + 31211205714 \, x^{2} + 13685553417 \, x + 2249141207}{105644 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} - \frac{509375}{121} \, \log \left (5 \, x + 3\right ) + \frac{70752609}{16807} \, \log \left (3 \, x + 2\right ) - \frac{64}{2033647} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^5*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217267, size = 200, normalized size = 2.33 \[ -\frac{924595208460 \, x^{4} + 2434767448806 \, x^{3} + 2403262839978 \, x^{2} + 34244262500 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (5 \, x + 3\right ) - 34244262756 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (3 \, x + 2\right ) + 256 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )} \log \left (2 \, x - 1\right ) + 1053787613109 \, x + 173183872939}{8134588 \,{\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^5*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.686339, size = 75, normalized size = 0.87 \[ - \frac{12007729980 x^{4} + 31620356478 x^{3} + 31211205714 x^{2} + 13685553417 x + 2249141207}{42785820 x^{5} + 139767012 x^{4} + 182552832 x^{3} + 119166432 x^{2} + 38876992 x + 5070912} - \frac{64 \log{\left (x - \frac{1}{2} \right )}}{2033647} - \frac{509375 \log{\left (x + \frac{3}{5} \right )}}{121} + \frac{70752609 \log{\left (x + \frac{2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**5/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.213989, size = 111, normalized size = 1.29 \[ -\frac{3125}{11 \,{\left (5 \, x + 3\right )}} + \frac{135 \,{\left (\frac{34747884}{5 \, x + 3} + \frac{13347468}{{\left (5 \, x + 3\right )}^{2}} + \frac{1775512}{{\left (5 \, x + 3\right )}^{3}} + 30897639\right )}}{9604 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{4}} + \frac{70752609}{16807} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{64}{2033647} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^5*(2*x - 1)),x, algorithm="giac")
[Out]