Optimal. Leaf size=97 \[ \frac{64}{3195731 (1-2 x)}+\frac{630342}{2401 (3 x+2)}+\frac{400000}{1331 (5 x+3)}+\frac{8829}{686 (3 x+2)^2}-\frac{3125}{242 (5 x+3)^2}+\frac{27}{49 (3 x+2)^3}-\frac{15168 \log (1-2 x)}{246071287}-\frac{37214802 \log (3 x+2)}{16807}+\frac{32418750 \log (5 x+3)}{14641} \]
[Out]
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Rubi [A] time = 0.116967, 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 \[ \frac{64}{3195731 (1-2 x)}+\frac{630342}{2401 (3 x+2)}+\frac{400000}{1331 (5 x+3)}+\frac{8829}{686 (3 x+2)^2}-\frac{3125}{242 (5 x+3)^2}+\frac{27}{49 (3 x+2)^3}-\frac{15168 \log (1-2 x)}{246071287}-\frac{37214802 \log (3 x+2)}{16807}+\frac{32418750 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 14.4917, size = 80, normalized size = 0.82 \[ - \frac{15168 \log{\left (- 2 x + 1 \right )}}{246071287} - \frac{37214802 \log{\left (3 x + 2 \right )}}{16807} + \frac{32418750 \log{\left (5 x + 3 \right )}}{14641} + \frac{400000}{1331 \left (5 x + 3\right )} - \frac{3125}{242 \left (5 x + 3\right )^{2}} + \frac{630342}{2401 \left (3 x + 2\right )} + \frac{8829}{686 \left (3 x + 2\right )^{2}} + \frac{27}{49 \left (3 x + 2\right )^{3}} + \frac{64}{3195731 \left (- 2 x + 1\right )} \]
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)**3,x)
[Out]
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Mathematica [A] time = 0.176378, size = 88, normalized size = 0.91 \[ \frac{2 \left (\frac{77}{4} \left (\frac{1677970404}{3 x+2}+\frac{1920800000}{5 x+3}+\frac{82259793}{(3 x+2)^2}-\frac{82534375}{(5 x+3)^2}+\frac{3521826}{(3 x+2)^3}+\frac{128}{1-2 x}\right )-7584 \log (1-2 x)-272430958041 \log (6 x+4)+272430965625 \log (10 x+6)\right )}{246071287} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.021, size = 80, normalized size = 0.8 \[ -{\frac{3125}{242\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{400000}{3993+6655\,x}}+{\frac{32418750\,\ln \left ( 3+5\,x \right ) }{14641}}+{\frac{27}{49\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{8829}{686\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{630342}{4802+7203\,x}}-{\frac{37214802\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{64}{-3195731+6391462\,x}}-{\frac{15168\,\ln \left ( -1+2\,x \right ) }{246071287}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^2/(2+3*x)^4/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34715, size = 113, normalized size = 1.16 \[ \frac{1273702595400 \, x^{5} + 2632318355880 \, x^{4} + 1509100957674 \, x^{3} - 229550032266 \, x^{2} - 456430279071 \, x - 107358241468}{6391462 \,{\left (1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right )}} + \frac{32418750}{14641} \, \log \left (5 \, x + 3\right ) - \frac{37214802}{16807} \, \log \left (3 \, x + 2\right ) - \frac{15168}{246071287} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218093, size = 234, normalized size = 2.41 \[ \frac{98075099845800 \, x^{5} + 202688513402760 \, x^{4} + 116200773740898 \, x^{3} - 17675352484482 \, x^{2} + 1089723862500 \,{\left (1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right )} \log \left (5 \, x + 3\right ) - 1089723832164 \,{\left (1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right )} \log \left (3 \, x + 2\right ) - 30336 \,{\left (1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right )} \log \left (2 \, x - 1\right ) - 35145131488467 \, x - 8266584593036}{492142574 \,{\left (1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.744115, size = 85, normalized size = 0.88 \[ \frac{1273702595400 x^{5} + 2632318355880 x^{4} + 1509100957674 x^{3} - 229550032266 x^{2} - 456430279071 x - 107358241468}{8628473700 x^{6} + 23296878990 x^{5} + 21513661092 x^{4} + 4915034278 x^{3} - 4077752756 x^{2} - 2684414040 x - 460185264} - \frac{15168 \log{\left (x - \frac{1}{2} \right )}}{246071287} + \frac{32418750 \log{\left (x + \frac{3}{5} \right )}}{14641} - \frac{37214802 \log{\left (x + \frac{2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**2/(2+3*x)**4/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.212556, size = 143, normalized size = 1.47 \[ -\frac{64}{3195731 \,{\left (2 \, x - 1\right )}} - \frac{4 \,{\left (\frac{49415890344165}{2 \, x - 1} + \frac{169212487575969}{{\left (2 \, x - 1\right )}^{2}} + \frac{257446971133345}{{\left (2 \, x - 1\right )}^{3}} + \frac{146840081089779}{{\left (2 \, x - 1\right )}^{4}} + 5410112162850\right )}}{246071287 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} - \frac{37214802}{16807} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) + \frac{32418750}{14641} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^3*(3*x + 2)^4*(2*x - 1)^2),x, algorithm="giac")
[Out]