Optimal. Leaf size=69 \[ -\frac{2187 x^4}{1000}-\frac{24543 x^3}{2500}-\frac{1044657 x^2}{50000}-\frac{339309 x}{10000}-\frac{233}{9453125 (5 x+3)}-\frac{1}{1718750 (5 x+3)^2}-\frac{823543 \log (1-2 x)}{42592}+\frac{4667 \log (5 x+3)}{20796875} \]
[Out]
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Rubi [A] time = 0.0767498, antiderivative size = 69, 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 \[ -\frac{2187 x^4}{1000}-\frac{24543 x^3}{2500}-\frac{1044657 x^2}{50000}-\frac{339309 x}{10000}-\frac{233}{9453125 (5 x+3)}-\frac{1}{1718750 (5 x+3)^2}-\frac{823543 \log (1-2 x)}{42592}+\frac{4667 \log (5 x+3)}{20796875} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{2187 x^{4}}{1000} - \frac{24543 x^{3}}{2500} - \frac{823543 \log{\left (- 2 x + 1 \right )}}{42592} + \frac{4667 \log{\left (5 x + 3 \right )}}{20796875} + \int \left (- \frac{339309}{10000}\right )\, dx - \frac{1044657 \int x\, dx}{25000} - \frac{233}{9453125 \left (5 x + 3\right )} - \frac{1}{1718750 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**7/(1-2*x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0596653, size = 60, normalized size = 0.87 \[ \frac{-\frac{11 \left (66156750000 x^6+376358400000 x^5+1012198275000 x^4+1891740015000 x^3+746752646475 x^2-485450731630 x-256487424349\right )}{(5 x+3)^2}-257357187500 \log (1-2 x)+2986880 \log (10 x+6)}{13310000000} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^7/((1 - 2*x)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.013, size = 54, normalized size = 0.8 \[ -{\frac{2187\,{x}^{4}}{1000}}-{\frac{24543\,{x}^{3}}{2500}}-{\frac{1044657\,{x}^{2}}{50000}}-{\frac{339309\,x}{10000}}-{\frac{1}{1718750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{233}{28359375+47265625\,x}}+{\frac{4667\,\ln \left ( 3+5\,x \right ) }{20796875}}-{\frac{823543\,\ln \left ( -1+2\,x \right ) }{42592}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^7/(1-2*x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.33482, size = 73, normalized size = 1.06 \[ -\frac{2187}{1000} \, x^{4} - \frac{24543}{2500} \, x^{3} - \frac{1044657}{50000} \, x^{2} - \frac{339309}{10000} \, x - \frac{2330 \, x + 1409}{18906250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{4667}{20796875} \, \log \left (5 \, x + 3\right ) - \frac{823543}{42592} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^7/((5*x + 3)^3*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214724, size = 108, normalized size = 1.57 \[ -\frac{181931062500 \, x^{6} + 1034985600000 \, x^{5} + 2783545256250 \, x^{4} + 5202285041250 \, x^{3} + 4012849402650 \, x^{2} - 746720 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 64339296875 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 1016146037830 \, x + 247984}{3327500000 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^7/((5*x + 3)^3*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.458771, size = 60, normalized size = 0.87 \[ - \frac{2187 x^{4}}{1000} - \frac{24543 x^{3}}{2500} - \frac{1044657 x^{2}}{50000} - \frac{339309 x}{10000} - \frac{2330 x + 1409}{472656250 x^{2} + 567187500 x + 170156250} - \frac{823543 \log{\left (x - \frac{1}{2} \right )}}{42592} + \frac{4667 \log{\left (x + \frac{3}{5} \right )}}{20796875} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**7/(1-2*x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.210345, size = 69, normalized size = 1. \[ -\frac{2187}{1000} \, x^{4} - \frac{24543}{2500} \, x^{3} - \frac{1044657}{50000} \, x^{2} - \frac{339309}{10000} \, x - \frac{2330 \, x + 1409}{18906250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{4667}{20796875} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{823543}{42592} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^7/((5*x + 3)^3*(2*x - 1)),x, algorithm="giac")
[Out]