Optimal. Leaf size=65 \[ \frac{144}{14641 (1-2 x)}-\frac{195}{14641 (5 x+3)}+\frac{7}{1331 (1-2 x)^2}-\frac{5}{2662 (5 x+3)^2}-\frac{1110 \log (1-2 x)}{161051}+\frac{1110 \log (5 x+3)}{161051} \]
[Out]
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Rubi [A] time = 0.068596, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{144}{14641 (1-2 x)}-\frac{195}{14641 (5 x+3)}+\frac{7}{1331 (1-2 x)^2}-\frac{5}{2662 (5 x+3)^2}-\frac{1110 \log (1-2 x)}{161051}+\frac{1110 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 9.87283, size = 53, normalized size = 0.82 \[ - \frac{1110 \log{\left (- 2 x + 1 \right )}}{161051} + \frac{1110 \log{\left (5 x + 3 \right )}}{161051} - \frac{195}{14641 \left (5 x + 3\right )} - \frac{5}{2662 \left (5 x + 3\right )^{2}} + \frac{144}{14641 \left (- 2 x + 1\right )} + \frac{7}{1331 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)/(1-2*x)**3/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0397905, size = 48, normalized size = 0.74 \[ \frac{\frac{11 \left (-22200 x^3-3330 x^2+11026 x+2753\right )}{\left (10 x^2+x-3\right )^2}-2220 \log (1-2 x)+2220 \log (5 x+3)}{322102} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)/((1 - 2*x)^3*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.014, size = 54, normalized size = 0.8 \[ -{\frac{5}{2662\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{195}{43923+73205\,x}}+{\frac{1110\,\ln \left ( 3+5\,x \right ) }{161051}}+{\frac{7}{1331\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{144}{-14641+29282\,x}}-{\frac{1110\,\ln \left ( -1+2\,x \right ) }{161051}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)/(1-2*x)^3/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35055, size = 76, normalized size = 1.17 \[ -\frac{22200 \, x^{3} + 3330 \, x^{2} - 11026 \, x - 2753}{29282 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{1110}{161051} \, \log \left (5 \, x + 3\right ) - \frac{1110}{161051} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20892, size = 128, normalized size = 1.97 \[ -\frac{244200 \, x^{3} + 36630 \, x^{2} - 2220 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2220 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 121286 \, x - 30283}{322102 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.421865, size = 54, normalized size = 0.83 \[ - \frac{22200 x^{3} + 3330 x^{2} - 11026 x - 2753}{2928200 x^{4} + 585640 x^{3} - 1727638 x^{2} - 175692 x + 263538} - \frac{1110 \log{\left (x - \frac{1}{2} \right )}}{161051} + \frac{1110 \log{\left (x + \frac{3}{5} \right )}}{161051} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)/(1-2*x)**3/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.212943, size = 62, normalized size = 0.95 \[ -\frac{22200 \, x^{3} + 3330 \, x^{2} - 11026 \, x - 2753}{29282 \,{\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac{1110}{161051} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1110}{161051} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="giac")
[Out]