Optimal. Leaf size=86 \[ \frac{4774713}{16807 (3 x+2)}+\frac{136419}{4802 (3 x+2)^2}+\frac{1299}{343 (3 x+2)^3}+\frac{111}{196 (3 x+2)^4}+\frac{3}{35 (3 x+2)^5}-\frac{64 \log (1-2 x)}{1294139}-\frac{167115051 \log (3 x+2)}{117649}+\frac{15625}{11} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0916118, 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 \[ \frac{4774713}{16807 (3 x+2)}+\frac{136419}{4802 (3 x+2)^2}+\frac{1299}{343 (3 x+2)^3}+\frac{111}{196 (3 x+2)^4}+\frac{3}{35 (3 x+2)^5}-\frac{64 \log (1-2 x)}{1294139}-\frac{167115051 \log (3 x+2)}{117649}+\frac{15625}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 12.461, size = 76, normalized size = 0.88 \[ - \frac{64 \log{\left (- 2 x + 1 \right )}}{1294139} - \frac{167115051 \log{\left (3 x + 2 \right )}}{117649} + \frac{15625 \log{\left (5 x + 3 \right )}}{11} + \frac{4774713}{16807 \left (3 x + 2\right )} + \frac{136419}{4802 \left (3 x + 2\right )^{2}} + \frac{1299}{343 \left (3 x + 2\right )^{3}} + \frac{111}{196 \left (3 x + 2\right )^{4}} + \frac{3}{35 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**6/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.111444, size = 60, normalized size = 0.7 \[ \frac{\frac{2079 \left (286482780 x^4+773503410 x^3+783477080 x^2+352854525 x+59622386\right )}{4 (3 x+2)^5}-320 \log (1-2 x)-9191327805 \log (6 x+4)+9191328125 \log (10 x+6)}{6470695} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^6*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.016, size = 71, normalized size = 0.8 \[{\frac{15625\,\ln \left ( 3+5\,x \right ) }{11}}+{\frac{3}{35\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{111}{196\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{1299}{343\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{136419}{4802\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{4774713}{33614+50421\,x}}-{\frac{167115051\,\ln \left ( 2+3\,x \right ) }{117649}}-{\frac{64\,\ln \left ( -1+2\,x \right ) }{1294139}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^6/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34108, size = 100, normalized size = 1.16 \[ \frac{27 \,{\left (286482780 \, x^{4} + 773503410 \, x^{3} + 783477080 \, x^{2} + 352854525 \, x + 59622386\right )}}{336140 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac{15625}{11} \, \log \left (5 \, x + 3\right ) - \frac{167115051}{117649} \, \log \left (3 \, x + 2\right ) - \frac{64}{1294139} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^6*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224273, size = 200, normalized size = 2.33 \[ \frac{595597699620 \, x^{4} + 1608113589390 \, x^{3} + 1628848849320 \, x^{2} + 36765312500 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 36765311220 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) - 1280 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 733584557475 \, x + 123954940494}{25882780 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^6*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.680154, size = 75, normalized size = 0.87 \[ \frac{7735035060 x^{4} + 20884592070 x^{3} + 21153881160 x^{2} + 9527072175 x + 1609804422}{81682020 x^{5} + 272273400 x^{4} + 363031200 x^{3} + 242020800 x^{2} + 80673600 x + 10756480} - \frac{64 \log{\left (x - \frac{1}{2} \right )}}{1294139} + \frac{15625 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{167115051 \log{\left (x + \frac{2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**6/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.208837, size = 77, normalized size = 0.9 \[ \frac{27 \,{\left (286482780 \, x^{4} + 773503410 \, x^{3} + 783477080 \, x^{2} + 352854525 \, x + 59622386\right )}}{336140 \,{\left (3 \, x + 2\right )}^{5}} + \frac{15625}{11} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{167115051}{117649} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{64}{1294139} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^6*(2*x - 1)),x, algorithm="giac")
[Out]