Optimal. Leaf size=64 \[ -\frac{648}{49 (3 x+2)}-\frac{125}{11 (5 x+3)}-\frac{9}{14 (3 x+2)^2}-\frac{16 \log (1-2 x)}{41503}+\frac{34371}{343} \log (3 x+2)-\frac{12125}{121} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0725955, antiderivative size = 64, 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 \[ -\frac{648}{49 (3 x+2)}-\frac{125}{11 (5 x+3)}-\frac{9}{14 (3 x+2)^2}-\frac{16 \log (1-2 x)}{41503}+\frac{34371}{343} \log (3 x+2)-\frac{12125}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 9.99033, size = 53, normalized size = 0.83 \[ - \frac{16 \log{\left (- 2 x + 1 \right )}}{41503} + \frac{34371 \log{\left (3 x + 2 \right )}}{343} - \frac{12125 \log{\left (5 x + 3 \right )}}{121} - \frac{125}{11 \left (5 x + 3\right )} - \frac{648}{49 \left (3 x + 2\right )} - \frac{9}{14 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0401041, size = 60, normalized size = 0.94 \[ -\frac{125}{55 x+33}-\frac{648}{147 x+98}-\frac{9}{14 (3 x+2)^2}-\frac{16 \log (1-2 x)}{41503}+\frac{34371}{343} \log (6 x+4)-\frac{12125}{121} \log (10 x+6) \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^3*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.015, size = 53, normalized size = 0.8 \[ -{\frac{125}{33+55\,x}}-{\frac{12125\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{9}{14\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{648}{98+147\,x}}+{\frac{34371\,\ln \left ( 2+3\,x \right ) }{343}}-{\frac{16\,\ln \left ( -1+2\,x \right ) }{41503}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.35373, size = 73, normalized size = 1.14 \[ -\frac{324090 \, x^{2} + 421329 \, x + 136615}{1078 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} - \frac{12125}{121} \, \log \left (5 \, x + 3\right ) + \frac{34371}{343} \, \log \left (3 \, x + 2\right ) - \frac{16}{41503} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^3*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217562, size = 132, normalized size = 2.06 \[ -\frac{24954930 \, x^{2} + 8317750 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 8317782 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 32 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (2 \, x - 1\right ) + 32442333 \, x + 10519355}{83006 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^3*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.561996, size = 54, normalized size = 0.84 \[ - \frac{324090 x^{2} + 421329 x + 136615}{48510 x^{3} + 93786 x^{2} + 60368 x + 12936} - \frac{16 \log{\left (x - \frac{1}{2} \right )}}{41503} - \frac{12125 \log{\left (x + \frac{3}{5} \right )}}{121} + \frac{34371 \log{\left (x + \frac{2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.212143, size = 86, normalized size = 1.34 \[ -\frac{125}{11 \,{\left (5 \, x + 3\right )}} + \frac{135 \,{\left (\frac{214}{5 \, x + 3} + 537\right )}}{98 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{2}} + \frac{34371}{343} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{16}{41503} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^3*(2*x - 1)),x, algorithm="giac")
[Out]