Optimal. Leaf size=86 \[ \frac{204228}{343 (3 x+2)}+\frac{81250}{121 (5 x+3)}+\frac{2889}{98 (3 x+2)^2}-\frac{625}{22 (5 x+3)^2}+\frac{9}{7 (3 x+2)^3}-\frac{64 \log (1-2 x)}{3195731}-\frac{11984706 \log (3 x+2)}{2401}+\frac{6643750 \log (5 x+3)}{1331} \]
[Out]
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Rubi [A] time = 0.0981525, 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 \[ \frac{204228}{343 (3 x+2)}+\frac{81250}{121 (5 x+3)}+\frac{2889}{98 (3 x+2)^2}-\frac{625}{22 (5 x+3)^2}+\frac{9}{7 (3 x+2)^3}-\frac{64 \log (1-2 x)}{3195731}-\frac{11984706 \log (3 x+2)}{2401}+\frac{6643750 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 12.9219, size = 73, normalized size = 0.85 \[ - \frac{64 \log{\left (- 2 x + 1 \right )}}{3195731} - \frac{11984706 \log{\left (3 x + 2 \right )}}{2401} + \frac{6643750 \log{\left (5 x + 3 \right )}}{1331} + \frac{81250}{121 \left (5 x + 3\right )} - \frac{625}{22 \left (5 x + 3\right )^{2}} + \frac{204228}{343 \left (3 x + 2\right )} + \frac{2889}{98 \left (3 x + 2\right )^{2}} + \frac{9}{7 \left (3 x + 2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**4/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0515576, size = 84, normalized size = 0.98 \[ \frac{204228}{343 (3 x+2)}+\frac{81250}{605 x+363}+\frac{2889}{98 (3 x+2)^2}-\frac{625}{22 (5 x+3)^2}+\frac{9}{7 (3 x+2)^3}-\frac{64 \log (1-2 x)}{3195731}-\frac{11984706 \log (6 x+4)}{2401}+\frac{6643750 \log (10 x+6)}{1331} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.017, size = 71, normalized size = 0.8 \[ -{\frac{625}{22\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{81250}{363+605\,x}}+{\frac{6643750\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{9}{7\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{2889}{98\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{204228}{686+1029\,x}}-{\frac{11984706\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{64\,\ln \left ( -1+2\,x \right ) }{3195731}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^4/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.3409, size = 100, normalized size = 1.16 \[ \frac{18644777100 \, x^{4} + 47854927170 \, x^{3} + 46018070136 \, x^{2} + 19648830809 \, x + 3143075528}{83006 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + \frac{6643750}{1331} \, \log \left (5 \, x + 3\right ) - \frac{11984706}{2401} \, \log \left (3 \, x + 2\right ) - \frac{64}{3195731} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223319, size = 200, normalized size = 2.33 \[ \frac{1435647836700 \, x^{4} + 3684829392090 \, x^{3} + 3543391400472 \, x^{2} + 31903287500 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 31903287372 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) - 128 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (2 \, x - 1\right ) + 1512959972293 \, x + 242016815656}{6391462 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.712048, size = 75, normalized size = 0.87 \[ \frac{18644777100 x^{4} + 47854927170 x^{3} + 46018070136 x^{2} + 19648830809 x + 3143075528}{56029050 x^{5} + 179292960 x^{4} + 229345578 x^{3} + 146588596 x^{2} + 46815384 x + 5976432} - \frac{64 \log{\left (x - \frac{1}{2} \right )}}{3195731} + \frac{6643750 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{11984706 \log{\left (x + \frac{2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**4/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.208931, size = 86, normalized size = 1. \[ \frac{18644777100 \, x^{4} + 47854927170 \, x^{3} + 46018070136 \, x^{2} + 19648830809 \, x + 3143075528}{83006 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{3}} + \frac{6643750}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{11984706}{2401} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{64}{3195731} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)),x, algorithm="giac")
[Out]