Optimal. Leaf size=86 \[ \frac{2704}{3195731 (1-2 x)}-\frac{6156}{2401 (3 x+2)}-\frac{3125}{1331 (5 x+3)}+\frac{8}{41503 (1-2 x)^2}-\frac{81}{686 (3 x+2)^2}-\frac{274224 \log (1-2 x)}{246071287}+\frac{333639 \log (3 x+2)}{16807}-\frac{290625 \log (5 x+3)}{14641} \]
[Out]
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Rubi [A] time = 0.104244, 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 \[ \frac{2704}{3195731 (1-2 x)}-\frac{6156}{2401 (3 x+2)}-\frac{3125}{1331 (5 x+3)}+\frac{8}{41503 (1-2 x)^2}-\frac{81}{686 (3 x+2)^2}-\frac{274224 \log (1-2 x)}{246071287}+\frac{333639 \log (3 x+2)}{16807}-\frac{290625 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 12.7818, size = 70, normalized size = 0.81 \[ - \frac{274224 \log{\left (- 2 x + 1 \right )}}{246071287} + \frac{333639 \log{\left (3 x + 2 \right )}}{16807} - \frac{290625 \log{\left (5 x + 3 \right )}}{14641} - \frac{3125}{1331 \left (5 x + 3\right )} - \frac{6156}{2401 \left (3 x + 2\right )} - \frac{81}{686 \left (3 x + 2\right )^{2}} + \frac{2704}{3195731 \left (- 2 x + 1\right )} + \frac{8}{41503 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**3/(2+3*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.10309, size = 74, normalized size = 0.86 \[ \frac{\frac{41503 (6558 x-3251)}{\left (6 x^2+x-2\right )^2}-\frac{154 (16395384 x-7937593)}{6 x^2+x-2}-\frac{1155481250}{5 x+3}-548448 \log (5-10 x)+9769617198 \log (5 (3 x+2))-9769068750 \log (5 x+3)}{492142574} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^3*(2 + 3*x)^3*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.02, size = 71, normalized size = 0.8 \[ -{\frac{3125}{3993+6655\,x}}-{\frac{290625\,\ln \left ( 3+5\,x \right ) }{14641}}-{\frac{81}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{6156}{4802+7203\,x}}+{\frac{333639\,\ln \left ( 2+3\,x \right ) }{16807}}+{\frac{8}{41503\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{2704}{-3195731+6391462\,x}}-{\frac{274224\,\ln \left ( -1+2\,x \right ) }{246071287}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^3/(2+3*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.35141, size = 100, normalized size = 1.16 \[ -\frac{1523948040 \, x^{4} + 458007084 \, x^{3} - 957482214 \, x^{2} - 147486147 \, x + 160532983}{6391462 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )}} - \frac{290625}{14641} \, \log \left (5 \, x + 3\right ) + \frac{333639}{16807} \, \log \left (3 \, x + 2\right ) - \frac{274224}{246071287} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^3*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209767, size = 200, normalized size = 2.33 \[ -\frac{117343999080 \, x^{4} + 35266545468 \, x^{3} - 73726130478 \, x^{2} + 9769068750 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 9769617198 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 548448 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )} \log \left (2 \, x - 1\right ) - 11356433319 \, x + 12361039691}{492142574 \,{\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^3*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.675925, size = 75, normalized size = 0.87 \[ - \frac{1523948040 x^{4} + 458007084 x^{3} - 957482214 x^{2} - 147486147 x + 160532983}{1150463160 x^{5} + 1073765616 x^{4} - 504925498 x^{3} - 568840118 x^{2} + 51131696 x + 76697544} - \frac{274224 \log{\left (x - \frac{1}{2} \right )}}{246071287} - \frac{290625 \log{\left (x + \frac{3}{5} \right )}}{14641} + \frac{333639 \log{\left (x + \frac{2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**3/(2+3*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.220886, size = 128, normalized size = 1.49 \[ -\frac{3125}{1331 \,{\left (5 \, x + 3\right )}} - \frac{5 \,{\left (\frac{84659379036}{5 \, x + 3} - \frac{206753119043}{{\left (5 \, x + 3\right )}^{2}} - \frac{95568773322}{{\left (5 \, x + 3\right )}^{3}} - 7983405324\right )}}{70306082 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}{\left (\frac{1}{5 \, x + 3} + 3\right )}^{2}} + \frac{333639}{16807} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{274224}{246071287} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^3*(2*x - 1)^3),x, algorithm="giac")
[Out]