Optimal. Leaf size=87 \[ -\frac{968}{117649 (3 x+2)}-\frac{242}{16807 (3 x+2)^2}-\frac{242}{7203 (3 x+2)^3}-\frac{121}{1372 (3 x+2)^4}+\frac{68}{2205 (3 x+2)^5}-\frac{1}{378 (3 x+2)^6}-\frac{1936 \log (1-2 x)}{823543}+\frac{1936 \log (3 x+2)}{823543} \]
[Out]
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Rubi [A] time = 0.0863132, antiderivative size = 87, 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 \[ -\frac{968}{117649 (3 x+2)}-\frac{242}{16807 (3 x+2)^2}-\frac{242}{7203 (3 x+2)^3}-\frac{121}{1372 (3 x+2)^4}+\frac{68}{2205 (3 x+2)^5}-\frac{1}{378 (3 x+2)^6}-\frac{1936 \log (1-2 x)}{823543}+\frac{1936 \log (3 x+2)}{823543} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^7),x]
[Out]
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Rubi in Sympy [A] time = 12.7063, size = 76, normalized size = 0.87 \[ - \frac{1936 \log{\left (- 2 x + 1 \right )}}{823543} + \frac{1936 \log{\left (3 x + 2 \right )}}{823543} - \frac{968}{117649 \left (3 x + 2\right )} - \frac{242}{16807 \left (3 x + 2\right )^{2}} - \frac{242}{7203 \left (3 x + 2\right )^{3}} - \frac{121}{1372 \left (3 x + 2\right )^{4}} + \frac{68}{2205 \left (3 x + 2\right )^{5}} - \frac{1}{378 \left (3 x + 2\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)/(2+3*x)**7,x)
[Out]
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Mathematica [A] time = 0.0703947, size = 57, normalized size = 0.66 \[ \frac{4 \left (-\frac{7 \left (127020960 x^5+497498760 x^4+819755640 x^3+739632465 x^2+351466812 x+67099978\right )}{16 (3 x+2)^6}-65340 \log (1-2 x)+65340 \log (6 x+4)\right )}{111178305} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/((1 - 2*x)*(2 + 3*x)^7),x]
[Out]
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Maple [A] time = 0.011, size = 72, normalized size = 0.8 \[ -{\frac{1}{378\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{68}{2205\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{121}{1372\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{242}{7203\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{242}{16807\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{968}{235298+352947\,x}}+{\frac{1936\,\ln \left ( 2+3\,x \right ) }{823543}}-{\frac{1936\,\ln \left ( -1+2\,x \right ) }{823543}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)/(2+3*x)^7,x)
[Out]
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Maxima [A] time = 1.33197, size = 103, normalized size = 1.18 \[ -\frac{127020960 \, x^{5} + 497498760 \, x^{4} + 819755640 \, x^{3} + 739632465 \, x^{2} + 351466812 \, x + 67099978}{63530460 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + \frac{1936}{823543} \, \log \left (3 \, x + 2\right ) - \frac{1936}{823543} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^7*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212478, size = 182, normalized size = 2.09 \[ -\frac{889146720 \, x^{5} + 3482491320 \, x^{4} + 5738289480 \, x^{3} + 5177427255 \, x^{2} - 1045440 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 1045440 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (2 \, x - 1\right ) + 2460267684 \, x + 469699846}{444713220 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^7*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.577871, size = 75, normalized size = 0.86 \[ - \frac{127020960 x^{5} + 497498760 x^{4} + 819755640 x^{3} + 739632465 x^{2} + 351466812 x + 67099978}{46313705340 x^{6} + 185254821360 x^{5} + 308758035600 x^{4} + 274451587200 x^{3} + 137225793600 x^{2} + 36593544960 x + 4065949440} - \frac{1936 \log{\left (x - \frac{1}{2} \right )}}{823543} + \frac{1936 \log{\left (x + \frac{2}{3} \right )}}{823543} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)/(2+3*x)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.214475, size = 72, normalized size = 0.83 \[ -\frac{127020960 \, x^{5} + 497498760 \, x^{4} + 819755640 \, x^{3} + 739632465 \, x^{2} + 351466812 \, x + 67099978}{63530460 \,{\left (3 \, x + 2\right )}^{6}} + \frac{1936}{823543} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{1936}{823543} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2/((3*x + 2)^7*(2*x - 1)),x, algorithm="giac")
[Out]