Optimal. Leaf size=75 \[ \frac{2889}{49 (3 x+2)}+\frac{12125}{121 (5 x+3)}+\frac{27}{14 (3 x+2)^2}-\frac{125}{22 (5 x+3)^2}-\frac{32 \log (1-2 x)}{456533}-\frac{204228}{343} \log (3 x+2)+\frac{792500 \log (5 x+3)}{1331} \]
[Out]
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Rubi [A] time = 0.0856956, antiderivative size = 75, 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 \[ \frac{2889}{49 (3 x+2)}+\frac{12125}{121 (5 x+3)}+\frac{27}{14 (3 x+2)^2}-\frac{125}{22 (5 x+3)^2}-\frac{32 \log (1-2 x)}{456533}-\frac{204228}{343} \log (3 x+2)+\frac{792500 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 11.4499, size = 63, normalized size = 0.84 \[ - \frac{32 \log{\left (- 2 x + 1 \right )}}{456533} - \frac{204228 \log{\left (3 x + 2 \right )}}{343} + \frac{792500 \log{\left (5 x + 3 \right )}}{1331} + \frac{12125}{121 \left (5 x + 3\right )} - \frac{125}{22 \left (5 x + 3\right )^{2}} + \frac{2889}{49 \left (3 x + 2\right )} + \frac{27}{14 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**3/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0472141, size = 71, normalized size = 0.95 \[ \frac{2889}{147 x+98}+\frac{12125}{605 x+363}+\frac{27}{14 (3 x+2)^2}-\frac{125}{22 (5 x+3)^2}-\frac{32 \log (1-2 x)}{456533}-\frac{204228}{343} \log (6 x+4)+\frac{792500 \log (10 x+6)}{1331} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.018, size = 62, normalized size = 0.8 \[ -{\frac{125}{22\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{12125}{363+605\,x}}+{\frac{792500\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{27}{14\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{2889}{98+147\,x}}-{\frac{204228\,\ln \left ( 2+3\,x \right ) }{343}}-{\frac{32\,\ln \left ( -1+2\,x \right ) }{456533}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^3/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34642, size = 86, normalized size = 1.15 \[ \frac{105906600 \, x^{3} + 201222420 \, x^{2} + 127244576 \, x + 26779805}{11858 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + \frac{792500}{1331} \, \log \left (5 \, x + 3\right ) - \frac{204228}{343} \, \log \left (3 \, x + 2\right ) - \frac{32}{456533} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^3*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225066, size = 166, normalized size = 2.21 \[ \frac{8154808200 \, x^{3} + 15494126340 \, x^{2} + 543655000 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 543654936 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) - 64 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (2 \, x - 1\right ) + 9797832352 \, x + 2062044985}{913066 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^3*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.649162, size = 65, normalized size = 0.87 \[ \frac{105906600 x^{3} + 201222420 x^{2} + 127244576 x + 26779805}{2668050 x^{4} + 6759060 x^{3} + 6415178 x^{2} + 2703624 x + 426888} - \frac{32 \log{\left (x - \frac{1}{2} \right )}}{456533} + \frac{792500 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{204228 \log{\left (x + \frac{2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**3/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.210211, size = 80, normalized size = 1.07 \[ \frac{105906600 \, x^{3} + 201222420 \, x^{2} + 127244576 \, x + 26779805}{11858 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{2}} + \frac{792500}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{204228}{343} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{32}{456533} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^3*(2*x - 1)),x, algorithm="giac")
[Out]