Optimal. Leaf size=86 \[ \frac{32}{290521 (1-2 x)}-\frac{107109}{2401 (3 x+2)}-\frac{3125}{121 (5 x+3)}-\frac{999}{343 (3 x+2)^2}-\frac{9}{49 (3 x+2)^3}-\frac{6464 \log (1-2 x)}{22370117}+\frac{5050944 \log (3 x+2)}{16807}-\frac{400000 \log (5 x+3)}{1331} \]
[Out]
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Rubi [A] time = 0.103999, 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 \[ \frac{32}{290521 (1-2 x)}-\frac{107109}{2401 (3 x+2)}-\frac{3125}{121 (5 x+3)}-\frac{999}{343 (3 x+2)^2}-\frac{9}{49 (3 x+2)^3}-\frac{6464 \log (1-2 x)}{22370117}+\frac{5050944 \log (3 x+2)}{16807}-\frac{400000 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 12.8044, size = 70, normalized size = 0.81 \[ - \frac{6464 \log{\left (- 2 x + 1 \right )}}{22370117} + \frac{5050944 \log{\left (3 x + 2 \right )}}{16807} - \frac{400000 \log{\left (5 x + 3 \right )}}{1331} - \frac{3125}{121 \left (5 x + 3\right )} - \frac{107109}{2401 \left (3 x + 2\right )} - \frac{999}{343 \left (3 x + 2\right )^{2}} - \frac{9}{49 \left (3 x + 2\right )^{3}} + \frac{32}{290521 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**2/(2+3*x)**4/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.145458, size = 70, normalized size = 0.81 \[ \frac{-\frac{77 \left (1571590080 x^4+2305013328 x^3+479067048 x^2-570653522 x-220783501\right )}{(3 x+2)^3 \left (10 x^2+x-3\right )}-6464 \log (3-6 x)+6722806464 \log (3 x+2)-6722800000 \log (-3 (5 x+3))}{22370117} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.02, size = 71, normalized size = 0.8 \[ -{\frac{3125}{363+605\,x}}-{\frac{400000\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{9}{49\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{999}{343\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{107109}{4802+7203\,x}}+{\frac{5050944\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{32}{-290521+581042\,x}}-{\frac{6464\,\ln \left ( -1+2\,x \right ) }{22370117}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^2/(2+3*x)^4/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34419, size = 100, normalized size = 1.16 \[ -\frac{1571590080 \, x^{4} + 2305013328 \, x^{3} + 479067048 \, x^{2} - 570653522 \, x - 220783501}{290521 \,{\left (270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right )}} - \frac{400000}{1331} \, \log \left (5 \, x + 3\right ) + \frac{5050944}{16807} \, \log \left (3 \, x + 2\right ) - \frac{6464}{22370117} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217429, size = 200, normalized size = 2.33 \[ -\frac{121012436160 \, x^{4} + 177486026256 \, x^{3} + 36888162696 \, x^{2} + 6722800000 \,{\left (270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right )} \log \left (5 \, x + 3\right ) - 6722806464 \,{\left (270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right )} \log \left (3 \, x + 2\right ) + 6464 \,{\left (270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right )} \log \left (2 \, x - 1\right ) - 43940321194 \, x - 17000329577}{22370117 \,{\left (270 \, x^{5} + 567 \, x^{4} + 333 \, x^{3} - 46 \, x^{2} - 100 \, x - 24\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.672036, size = 75, normalized size = 0.87 \[ - \frac{1571590080 x^{4} + 2305013328 x^{3} + 479067048 x^{2} - 570653522 x - 220783501}{78440670 x^{5} + 164725407 x^{4} + 96743493 x^{3} - 13363966 x^{2} - 29052100 x - 6972504} - \frac{6464 \log{\left (x - \frac{1}{2} \right )}}{22370117} - \frac{400000 \log{\left (x + \frac{3}{5} \right )}}{1331} + \frac{5050944 \log{\left (x + \frac{2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**2/(2+3*x)**4/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.210096, size = 128, normalized size = 1.49 \[ -\frac{3125}{121 \,{\left (5 \, x + 3\right )}} + \frac{5 \,{\left (\frac{52083388017}{5 \, x + 3} + \frac{44729490744}{{\left (5 \, x + 3\right )}^{2}} + \frac{9228837286}{{\left (5 \, x + 3\right )}^{3}} - 11003835798\right )}}{3195731 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}{\left (\frac{1}{5 \, x + 3} + 3\right )}^{3}} + \frac{5050944}{16807} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{6464}{22370117} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^2*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="giac")
[Out]