Optimal. Leaf size=98 \[ -\frac{352}{823543 (3 x+2)}-\frac{88}{117649 (3 x+2)^2}-\frac{88}{50421 (3 x+2)^3}-\frac{11}{2401 (3 x+2)^4}-\frac{22}{1715 (3 x+2)^5}-\frac{11}{294 (3 x+2)^6}+\frac{1}{147 (3 x+2)^7}-\frac{704 \log (1-2 x)}{5764801}+\frac{704 \log (3 x+2)}{5764801} \]
[Out]
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Rubi [A] time = 0.0835661, antiderivative size = 98, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{352}{823543 (3 x+2)}-\frac{88}{117649 (3 x+2)^2}-\frac{88}{50421 (3 x+2)^3}-\frac{11}{2401 (3 x+2)^4}-\frac{22}{1715 (3 x+2)^5}-\frac{11}{294 (3 x+2)^6}+\frac{1}{147 (3 x+2)^7}-\frac{704 \log (1-2 x)}{5764801}+\frac{704 \log (3 x+2)}{5764801} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^8),x]
[Out]
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Rubi in Sympy [A] time = 13.4227, size = 87, normalized size = 0.89 \[ - \frac{704 \log{\left (- 2 x + 1 \right )}}{5764801} + \frac{704 \log{\left (3 x + 2 \right )}}{5764801} - \frac{352}{823543 \left (3 x + 2\right )} - \frac{88}{117649 \left (3 x + 2\right )^{2}} - \frac{88}{50421 \left (3 x + 2\right )^{3}} - \frac{11}{2401 \left (3 x + 2\right )^{4}} - \frac{22}{1715 \left (3 x + 2\right )^{5}} - \frac{11}{294 \left (3 x + 2\right )^{6}} + \frac{1}{147 \left (3 x + 2\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(1-2*x)/(2+3*x)**8,x)
[Out]
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Mathematica [A] time = 0.0700923, size = 60, normalized size = 0.61 \[ \frac{-\frac{7 \left (7698240 x^6+35283600 x^5+69783120 x^4+77947650 x^3+54393768 x^2+25308459 x+5811068\right )}{(3 x+2)^7}-21120 \log (3-6 x)+21120 \log (3 x+2)}{172944030} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/((1 - 2*x)*(2 + 3*x)^8),x]
[Out]
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Maple [A] time = 0.013, size = 81, normalized size = 0.8 \[{\frac{1}{147\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{11}{294\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{22}{1715\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{11}{2401\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{88}{50421\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{88}{117649\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{352}{1647086+2470629\,x}}+{\frac{704\,\ln \left ( 2+3\,x \right ) }{5764801}}-{\frac{704\,\ln \left ( -1+2\,x \right ) }{5764801}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(1-2*x)/(2+3*x)^8,x)
[Out]
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Maxima [A] time = 1.35136, size = 116, normalized size = 1.18 \[ -\frac{7698240 \, x^{6} + 35283600 \, x^{5} + 69783120 \, x^{4} + 77947650 \, x^{3} + 54393768 \, x^{2} + 25308459 \, x + 5811068}{24706290 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + \frac{704}{5764801} \, \log \left (3 \, x + 2\right ) - \frac{704}{5764801} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^8*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222198, size = 209, normalized size = 2.13 \[ -\frac{53887680 \, x^{6} + 246985200 \, x^{5} + 488481840 \, x^{4} + 545633550 \, x^{3} + 380756376 \, x^{2} - 21120 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (3 \, x + 2\right ) + 21120 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (2 \, x - 1\right ) + 177159213 \, x + 40677476}{172944030 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^8*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.601125, size = 85, normalized size = 0.87 \[ - \frac{7698240 x^{6} + 35283600 x^{5} + 69783120 x^{4} + 77947650 x^{3} + 54393768 x^{2} + 25308459 x + 5811068}{54032656230 x^{7} + 252152395740 x^{6} + 504304791480 x^{5} + 560338657200 x^{4} + 373559104800 x^{3} + 149423641920 x^{2} + 33205253760 x + 3162405120} - \frac{704 \log{\left (x - \frac{1}{2} \right )}}{5764801} + \frac{704 \log{\left (x + \frac{2}{3} \right )}}{5764801} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)/(1-2*x)/(2+3*x)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.210729, size = 78, normalized size = 0.8 \[ -\frac{7698240 \, x^{6} + 35283600 \, x^{5} + 69783120 \, x^{4} + 77947650 \, x^{3} + 54393768 \, x^{2} + 25308459 \, x + 5811068}{24706290 \,{\left (3 \, x + 2\right )}^{7}} + \frac{704}{5764801} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{704}{5764801} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^8*(2*x - 1)),x, algorithm="giac")
[Out]