Optimal. Leaf size=76 \[ -\frac{6561 x^5}{1250}-\frac{264627 x^4}{10000}-\frac{1535517 x^3}{25000}-\frac{9268263 x^2}{100000}-\frac{62934003 x}{500000}-\frac{266}{47265625 (5 x+3)}-\frac{1}{8593750 (5 x+3)^2}-\frac{5764801 \log (1-2 x)}{85184}+\frac{31024 \log (5 x+3)}{519921875} \]
[Out]
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Rubi [A] time = 0.0850748, antiderivative size = 76, 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 \[ -\frac{6561 x^5}{1250}-\frac{264627 x^4}{10000}-\frac{1535517 x^3}{25000}-\frac{9268263 x^2}{100000}-\frac{62934003 x}{500000}-\frac{266}{47265625 (5 x+3)}-\frac{1}{8593750 (5 x+3)^2}-\frac{5764801 \log (1-2 x)}{85184}+\frac{31024 \log (5 x+3)}{519921875} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{6561 x^{5}}{1250} - \frac{264627 x^{4}}{10000} - \frac{1535517 x^{3}}{25000} - \frac{5764801 \log{\left (- 2 x + 1 \right )}}{85184} + \frac{31024 \log{\left (5 x + 3 \right )}}{519921875} + \int \left (- \frac{62934003}{500000}\right )\, dx - \frac{9268263 \int x\, dx}{50000} - \frac{266}{47265625 \left (5 x + 3\right )} - \frac{1}{8593750 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**8/(1-2*x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.164518, size = 68, normalized size = 0.89 \[ \frac{22 \left (-7938810000 x^5-40024833750 x^4-92898778500 x^3-140182477875 x^2-190375359075 x-\frac{8512}{5 x+3}-\frac{176}{(5 x+3)^2}-85278446550\right )-2251875390625 \log (3-6 x)+1985536 \log (-3 (5 x+3))}{33275000000} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^8/((1 - 2*x)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.013, size = 59, normalized size = 0.8 \[ -{\frac{6561\,{x}^{5}}{1250}}-{\frac{264627\,{x}^{4}}{10000}}-{\frac{1535517\,{x}^{3}}{25000}}-{\frac{9268263\,{x}^{2}}{100000}}-{\frac{62934003\,x}{500000}}-{\frac{1}{8593750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{266}{141796875+236328125\,x}}+{\frac{31024\,\ln \left ( 3+5\,x \right ) }{519921875}}-{\frac{5764801\,\ln \left ( -1+2\,x \right ) }{85184}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^8/(1-2*x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34674, size = 80, normalized size = 1.05 \[ -\frac{6561}{1250} \, x^{5} - \frac{264627}{10000} \, x^{4} - \frac{1535517}{25000} \, x^{3} - \frac{9268263}{100000} \, x^{2} - \frac{62934003}{500000} \, x - \frac{2660 \, x + 1607}{94531250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{31024}{519921875} \, \log \left (5 \, x + 3\right ) - \frac{5764801}{85184} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)^3*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215475, size = 115, normalized size = 1.51 \[ -\frac{4366345500000 \, x^{7} + 27253273162500 \, x^{6} + 79082602830000 \, x^{5} + 146338473723750 \, x^{4} + 215620841031750 \, x^{3} + 153403867608750 \, x^{2} - 1985536 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2251875390625 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 37694322033170 \, x + 565664}{33275000000 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)^3*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.473691, size = 66, normalized size = 0.87 \[ - \frac{6561 x^{5}}{1250} - \frac{264627 x^{4}}{10000} - \frac{1535517 x^{3}}{25000} - \frac{9268263 x^{2}}{100000} - \frac{62934003 x}{500000} - \frac{2660 x + 1607}{2363281250 x^{2} + 2835937500 x + 850781250} - \frac{5764801 \log{\left (x - \frac{1}{2} \right )}}{85184} + \frac{31024 \log{\left (x + \frac{3}{5} \right )}}{519921875} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**8/(1-2*x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.207375, size = 76, normalized size = 1. \[ -\frac{6561}{1250} \, x^{5} - \frac{264627}{10000} \, x^{4} - \frac{1535517}{25000} \, x^{3} - \frac{9268263}{100000} \, x^{2} - \frac{62934003}{500000} \, x - \frac{2660 \, x + 1607}{94531250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{31024}{519921875} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{5764801}{85184} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)^3*(2*x - 1)),x, algorithm="giac")
[Out]