Optimal. Leaf size=97 \[ \frac{11984706}{2401 (3 x+2)}+\frac{509375}{121 (5 x+3)}+\frac{102114}{343 (3 x+2)^2}-\frac{3125}{22 (5 x+3)^2}+\frac{963}{49 (3 x+2)^3}+\frac{27}{28 (3 x+2)^4}-\frac{128 \log (1-2 x)}{22370117}-\frac{631722537 \log (3 x+2)}{16807}+\frac{50028125 \log (5 x+3)}{1331} \]
[Out]
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Rubi [A] time = 0.114472, antiderivative size = 97, 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 \[ \frac{11984706}{2401 (3 x+2)}+\frac{509375}{121 (5 x+3)}+\frac{102114}{343 (3 x+2)^2}-\frac{3125}{22 (5 x+3)^2}+\frac{963}{49 (3 x+2)^3}+\frac{27}{28 (3 x+2)^4}-\frac{128 \log (1-2 x)}{22370117}-\frac{631722537 \log (3 x+2)}{16807}+\frac{50028125 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 14.4331, size = 83, normalized size = 0.86 \[ - \frac{128 \log{\left (- 2 x + 1 \right )}}{22370117} - \frac{631722537 \log{\left (3 x + 2 \right )}}{16807} + \frac{50028125 \log{\left (5 x + 3 \right )}}{1331} + \frac{509375}{121 \left (5 x + 3\right )} - \frac{3125}{22 \left (5 x + 3\right )^{2}} + \frac{11984706}{2401 \left (3 x + 2\right )} + \frac{102114}{343 \left (3 x + 2\right )^{2}} + \frac{963}{49 \left (3 x + 2\right )^{3}} + \frac{27}{28 \left (3 x + 2\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**5/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0613491, size = 95, normalized size = 0.98 \[ \frac{11984706}{2401 (3 x+2)}+\frac{509375}{605 x+363}+\frac{102114}{343 (3 x+2)^2}-\frac{3125}{22 (5 x+3)^2}+\frac{963}{49 (3 x+2)^3}+\frac{27}{28 (3 x+2)^4}-\frac{128 \log (1-2 x)}{22370117}-\frac{631722537 \log (6 x+4)}{16807}+\frac{50028125 \log (10 x+6)}{1331} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^5*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.017, size = 80, normalized size = 0.8 \[ -{\frac{3125}{22\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{509375}{363+605\,x}}+{\frac{50028125\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{27}{28\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{963}{49\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{102114}{343\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{11984706}{4802+7203\,x}}-{\frac{631722537\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{128\,\ln \left ( -1+2\,x \right ) }{22370117}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^5/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34087, size = 113, normalized size = 1.16 \[ \frac{5896678637700 \, x^{5} + 19065927586590 \, x^{4} + 24643748766492 \, x^{3} + 15916809968421 \, x^{2} + 5136860261578 \, x + 662695553413}{1162084 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + \frac{50028125}{1331} \, \log \left (5 \, x + 3\right ) - \frac{631722537}{16807} \, \log \left (3 \, x + 2\right ) - \frac{128}{22370117} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^5*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229201, size = 234, normalized size = 2.41 \[ \frac{454044255102900 \, x^{5} + 1468076424167430 \, x^{4} + 1897568655019884 \, x^{3} + 1225594367568417 \, x^{2} + 3363290787500 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 3363290786988 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) - 512 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (2 \, x - 1\right ) + 395538240141506 \, x + 51027557612801}{89480468 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^5*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.760671, size = 85, normalized size = 0.88 \[ \frac{5896678637700 x^{5} + 19065927586590 x^{4} + 24643748766492 x^{3} + 15916809968421 x^{2} + 5136860261578 x + 662695553413}{2353220100 x^{6} + 9099117720 x^{5} + 14652717156 x^{4} + 12578397216 x^{3} + 6070726816 x^{2} + 1561840896 x + 167340096} - \frac{128 \log{\left (x - \frac{1}{2} \right )}}{22370117} + \frac{50028125 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{631722537 \log{\left (x + \frac{2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**5/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.211489, size = 123, normalized size = 1.27 \[ \frac{11984706}{2401 \,{\left (3 \, x + 2\right )}} - \frac{46875 \,{\left (\frac{392}{3 \, x + 2} - 1795\right )}}{242 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + \frac{102114}{343 \,{\left (3 \, x + 2\right )}^{2}} + \frac{963}{49 \,{\left (3 \, x + 2\right )}^{3}} + \frac{27}{28 \,{\left (3 \, x + 2\right )}^{4}} + \frac{50028125}{1331} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{128}{22370117} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^5*(2*x - 1)),x, algorithm="giac")
[Out]