Optimal. Leaf size=75 \[ \frac{1104}{717409 (1-2 x)}+\frac{3375}{14641 (5 x+3)}+\frac{4}{9317 (1-2 x)^2}-\frac{125}{2662 (5 x+3)^2}-\frac{95232 \log (1-2 x)}{55240493}-\frac{243}{343} \log (3 x+2)+\frac{114375 \log (5 x+3)}{161051} \]
[Out]
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Rubi [A] time = 0.0888151, antiderivative size = 75, 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 \[ \frac{1104}{717409 (1-2 x)}+\frac{3375}{14641 (5 x+3)}+\frac{4}{9317 (1-2 x)^2}-\frac{125}{2662 (5 x+3)^2}-\frac{95232 \log (1-2 x)}{55240493}-\frac{243}{343} \log (3 x+2)+\frac{114375 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 11.5909, size = 63, normalized size = 0.84 \[ - \frac{95232 \log{\left (- 2 x + 1 \right )}}{55240493} - \frac{243 \log{\left (3 x + 2 \right )}}{343} + \frac{114375 \log{\left (5 x + 3 \right )}}{161051} + \frac{3375}{14641 \left (5 x + 3\right )} - \frac{125}{2662 \left (5 x + 3\right )^{2}} + \frac{1104}{717409 \left (- 2 x + 1\right )} + \frac{4}{9317 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**3/(2+3*x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.118596, size = 60, normalized size = 0.8 \[ -\frac{3 \left (-\frac{77 \left (6504600 x^3-2977380 x^2-2000774 x+950291\right )}{3 \left (10 x^2+x-3\right )^2}+63488 \log (3-6 x)+26090262 \log (3 x+2)-26153750 \log (-3 (5 x+3))\right )}{110480986} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^3*(2 + 3*x)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.017, size = 62, normalized size = 0.8 \[ -{\frac{125}{2662\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{3375}{43923+73205\,x}}+{\frac{114375\,\ln \left ( 3+5\,x \right ) }{161051}}-{\frac{243\,\ln \left ( 2+3\,x \right ) }{343}}+{\frac{4}{9317\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{1104}{-717409+1434818\,x}}-{\frac{95232\,\ln \left ( -1+2\,x \right ) }{55240493}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^3/(2+3*x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.3596, size = 86, normalized size = 1.15 \[ \frac{6504600 \, x^{3} - 2977380 \, x^{2} - 2000774 \, x + 950291}{1434818 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{114375}{161051} \, \log \left (5 \, x + 3\right ) - \frac{243}{343} \, \log \left (3 \, x + 2\right ) - \frac{95232}{55240493} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227755, size = 166, normalized size = 2.21 \[ \frac{500854200 \, x^{3} - 229258260 \, x^{2} + 78461250 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 78270786 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (3 \, x + 2\right ) - 190464 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 154059598 \, x + 73172407}{110480986 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.597871, size = 65, normalized size = 0.87 \[ \frac{6504600 x^{3} - 2977380 x^{2} - 2000774 x + 950291}{143481800 x^{4} + 28696360 x^{3} - 84654262 x^{2} - 8608908 x + 12913362} - \frac{95232 \log{\left (x - \frac{1}{2} \right )}}{55240493} + \frac{114375 \log{\left (x + \frac{3}{5} \right )}}{161051} - \frac{243 \log{\left (x + \frac{2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**3/(2+3*x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.213321, size = 80, normalized size = 1.07 \[ \frac{6504600 \, x^{3} - 2977380 \, x^{2} - 2000774 \, x + 950291}{1434818 \,{\left (5 \, x + 3\right )}^{2}{\left (2 \, x - 1\right )}^{2}} + \frac{114375}{161051} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{243}{343} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{95232}{55240493} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^3*(3*x + 2)*(2*x - 1)^3),x, algorithm="giac")
[Out]