Optimal. Leaf size=86 \[ \frac{2736}{5021863 (1-2 x)}+\frac{243}{343 (3 x+2)}+\frac{37500}{14641 (5 x+3)}+\frac{8}{65219 (1-2 x)^2}-\frac{625}{2662 (5 x+3)^2}-\frac{280752 \log (1-2 x)}{386683451}-\frac{26973 \log (3 x+2)}{2401}+\frac{1809375 \log (5 x+3)}{161051} \]
[Out]
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Rubi [A] time = 0.102502, 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 \[ \frac{2736}{5021863 (1-2 x)}+\frac{243}{343 (3 x+2)}+\frac{37500}{14641 (5 x+3)}+\frac{8}{65219 (1-2 x)^2}-\frac{625}{2662 (5 x+3)^2}-\frac{280752 \log (1-2 x)}{386683451}-\frac{26973 \log (3 x+2)}{2401}+\frac{1809375 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 13.0251, size = 70, normalized size = 0.81 \[ - \frac{280752 \log{\left (- 2 x + 1 \right )}}{386683451} - \frac{26973 \log{\left (3 x + 2 \right )}}{2401} + \frac{1809375 \log{\left (5 x + 3 \right )}}{161051} + \frac{37500}{14641 \left (5 x + 3\right )} - \frac{625}{2662 \left (5 x + 3\right )^{2}} + \frac{243}{343 \left (3 x + 2\right )} + \frac{2736}{5021863 \left (- 2 x + 1\right )} + \frac{8}{65219 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**3/(2+3*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.107967, size = 76, normalized size = 0.88 \[ -\frac{3 \left (-\frac{65219 (12290 x-6101)}{3 \left (10 x^2+x-3\right )^2}-\frac{154 (8570440 x-4446931)}{10 x^2+x-3}-\frac{182631834}{3 x+2}+187168 \log (3-6 x)+2896019082 \log (3 x+2)-2896206250 \log (-3 (5 x+3))\right )}{773366902} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^3*(2 + 3*x)^2*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.02, size = 71, normalized size = 0.8 \[ -{\frac{625}{2662\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{37500}{43923+73205\,x}}+{\frac{1809375\,\ln \left ( 3+5\,x \right ) }{161051}}+{\frac{243}{686+1029\,x}}-{\frac{26973\,\ln \left ( 2+3\,x \right ) }{2401}}+{\frac{8}{65219\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{2736}{-5021863+10043726\,x}}-{\frac{280752\,\ln \left ( -1+2\,x \right ) }{386683451}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^3/(2+3*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.35709, size = 100, normalized size = 1.16 \[ \frac{2254231800 \, x^{4} + 524583660 \, x^{3} - 1362222102 \, x^{2} - 159141275 \, x + 213794156}{10043726 \,{\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )}} + \frac{1809375}{161051} \, \log \left (5 \, x + 3\right ) - \frac{26973}{2401} \, \log \left (3 \, x + 2\right ) - \frac{280752}{386683451} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^2*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235172, size = 200, normalized size = 2.33 \[ \frac{173575848600 \, x^{4} + 40392941820 \, x^{3} - 104891101854 \, x^{2} + 8688618750 \,{\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 8688057246 \,{\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )} \log \left (3 \, x + 2\right ) - 561504 \,{\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )} \log \left (2 \, x - 1\right ) - 12253878175 \, x + 16462150012}{773366902 \,{\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^2*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.700732, size = 75, normalized size = 0.87 \[ \frac{2254231800 x^{4} + 524583660 x^{3} - 1362222102 x^{2} - 159141275 x + 213794156}{3013117800 x^{5} + 2611368760 x^{4} - 1375990462 x^{3} - 1365946736 x^{2} + 150655890 x + 180787068} - \frac{280752 \log{\left (x - \frac{1}{2} \right )}}{386683451} + \frac{1809375 \log{\left (x + \frac{3}{5} \right )}}{161051} - \frac{26973 \log{\left (x + \frac{2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**3/(2+3*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.211355, size = 128, normalized size = 1.49 \[ \frac{243}{343 \,{\left (3 \, x + 2\right )}} - \frac{9 \,{\left (\frac{55432245900}{3 \, x + 2} - \frac{106776659235}{{\left (3 \, x + 2\right )}^{2}} + \frac{22794463286}{{\left (3 \, x + 2\right )}^{3}} - 7652987500\right )}}{70306082 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}^{2}{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + \frac{1809375}{161051} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{280752}{386683451} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)^2*(2*x - 1)^3),x, algorithm="giac")
[Out]