Optimal. Leaf size=97 \[ \frac{64}{2033647 (1-2 x)}-\frac{5050944}{16807 (3 x+2)}-\frac{15625}{121 (5 x+3)}-\frac{107109}{4802 (3 x+2)^2}-\frac{666}{343 (3 x+2)^3}-\frac{27}{196 (3 x+2)^4}-\frac{15040 \log (1-2 x)}{156590819}+\frac{222359715 \log (3 x+2)}{117649}-\frac{2515625 \log (5 x+3)}{1331} \]
[Out]
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Rubi [A] time = 0.119111, 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 \[ \frac{64}{2033647 (1-2 x)}-\frac{5050944}{16807 (3 x+2)}-\frac{15625}{121 (5 x+3)}-\frac{107109}{4802 (3 x+2)^2}-\frac{666}{343 (3 x+2)^3}-\frac{27}{196 (3 x+2)^4}-\frac{15040 \log (1-2 x)}{156590819}+\frac{222359715 \log (3 x+2)}{117649}-\frac{2515625 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 14.2273, size = 80, normalized size = 0.82 \[ - \frac{15040 \log{\left (- 2 x + 1 \right )}}{156590819} + \frac{222359715 \log{\left (3 x + 2 \right )}}{117649} - \frac{2515625 \log{\left (5 x + 3 \right )}}{1331} - \frac{15625}{121 \left (5 x + 3\right )} - \frac{5050944}{16807 \left (3 x + 2\right )} - \frac{107109}{4802 \left (3 x + 2\right )^{2}} - \frac{666}{343 \left (3 x + 2\right )^{3}} - \frac{27}{196 \left (3 x + 2\right )^{4}} + \frac{64}{2033647 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**2/(2+3*x)**5/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.162597, size = 75, normalized size = 0.77 \[ \frac{-\frac{77 \left (830228340600 x^5+1771154199360 x^4+1064845635750 x^3-132753874800 x^2-317609203475 x-77754195847\right )}{(3 x+2)^4 \left (10 x^2+x-3\right )}-60160 \log (3-6 x)+1183843122660 \log (3 x+2)-1183843062500 \log (-3 (5 x+3))}{626363276} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^2*(2 + 3*x)^5*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.02, size = 80, normalized size = 0.8 \[ -{\frac{15625}{363+605\,x}}-{\frac{2515625\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{27}{196\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{666}{343\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{107109}{4802\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{5050944}{33614+50421\,x}}+{\frac{222359715\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{64}{-2033647+4067294\,x}}-{\frac{15040\,\ln \left ( -1+2\,x \right ) }{156590819}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^2/(2+3*x)^5/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34438, size = 113, normalized size = 1.16 \[ -\frac{830228340600 \, x^{5} + 1771154199360 \, x^{4} + 1064845635750 \, x^{3} - 132753874800 \, x^{2} - 317609203475 \, x - 77754195847}{8134588 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )}} - \frac{2515625}{1331} \, \log \left (5 \, x + 3\right ) + \frac{222359715}{117649} \, \log \left (3 \, x + 2\right ) - \frac{15040}{156590819} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^2*(3*x + 2)^5*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217106, size = 234, normalized size = 2.41 \[ -\frac{63927582226200 \, x^{5} + 136378873350720 \, x^{4} + 81993113952750 \, x^{3} - 10222048359600 \, x^{2} + 1183843062500 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (5 \, x + 3\right ) - 1183843122660 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (3 \, x + 2\right ) + 60160 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )} \log \left (2 \, x - 1\right ) - 24455908667575 \, x - 5987073080219}{626363276 \,{\left (810 \, x^{6} + 2241 \, x^{5} + 2133 \, x^{4} + 528 \, x^{3} - 392 \, x^{2} - 272 \, x - 48\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^2*(3*x + 2)^5*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.752707, size = 85, normalized size = 0.88 \[ - \frac{830228340600 x^{5} + 1771154199360 x^{4} + 1064845635750 x^{3} - 132753874800 x^{2} - 317609203475 x - 77754195847}{6589016280 x^{6} + 18229611708 x^{5} + 17351076204 x^{4} + 4295062464 x^{3} - 3188758496 x^{2} - 2212607936 x - 390460224} - \frac{15040 \log{\left (x - \frac{1}{2} \right )}}{156590819} - \frac{2515625 \log{\left (x + \frac{3}{5} \right )}}{1331} + \frac{222359715 \log{\left (x + \frac{2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**2/(2+3*x)**5/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.208272, size = 140, normalized size = 1.44 \[ -\frac{15625}{121 \,{\left (5 \, x + 3\right )}} + \frac{25 \,{\left (\frac{6062344264539}{5 \, x + 3} + \frac{7964082495612}{{\left (5 \, x + 3\right )}^{2}} + \frac{3205106234076}{{\left (5 \, x + 3\right )}^{3}} + \frac{435889532968}{{\left (5 \, x + 3\right )}^{4}} - 1385260555122\right )}}{89480468 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}{\left (\frac{1}{5 \, x + 3} + 3\right )}^{4}} + \frac{222359715}{117649} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{15040}{156590819} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^2*(3*x + 2)^5*(2*x - 1)^2),x, algorithm="giac")
[Out]