Optimal. Leaf size=73 \[ -\frac{729 x^6}{125}-\frac{51759 x^5}{3125}-\frac{181521 x^4}{12500}+\frac{2052 x^3}{3125}+\frac{129654 x^2}{15625}+\frac{1851147 x}{390625}-\frac{229}{1953125 (5 x+3)}-\frac{11}{3906250 (5 x+3)^2}+\frac{2037 \log (5 x+3)}{1953125} \]
[Out]
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Rubi [A] time = 0.0862981, antiderivative size = 73, 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 \[ -\frac{729 x^6}{125}-\frac{51759 x^5}{3125}-\frac{181521 x^4}{12500}+\frac{2052 x^3}{3125}+\frac{129654 x^2}{15625}+\frac{1851147 x}{390625}-\frac{229}{1953125 (5 x+3)}-\frac{11}{3906250 (5 x+3)^2}+\frac{2037 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{729 x^{6}}{125} - \frac{51759 x^{5}}{3125} - \frac{181521 x^{4}}{12500} + \frac{2052 x^{3}}{3125} + \frac{2037 \log{\left (5 x + 3 \right )}}{1953125} + \int \frac{1851147}{390625}\, dx + \frac{259308 \int x\, dx}{15625} - \frac{229}{1953125 \left (5 x + 3\right )} - \frac{11}{3906250 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)**7/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0379337, size = 64, normalized size = 0.88 \[ \frac{8148 \log (-3 (5 x+3))-\frac{5 \left (227812500 x^8+920362500 x^7+1425650625 x^6+887969250 x^5-150703875 x^4-583310700 x^3-372626040 x^2-107200136 x-12167374\right )}{(5 x+3)^2}}{7812500} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.01, size = 56, normalized size = 0.8 \[{\frac{1851147\,x}{390625}}+{\frac{129654\,{x}^{2}}{15625}}+{\frac{2052\,{x}^{3}}{3125}}-{\frac{181521\,{x}^{4}}{12500}}-{\frac{51759\,{x}^{5}}{3125}}-{\frac{729\,{x}^{6}}{125}}-{\frac{11}{3906250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{229}{5859375+9765625\,x}}+{\frac{2037\,\ln \left ( 3+5\,x \right ) }{1953125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)^7/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34261, size = 76, normalized size = 1.04 \[ -\frac{729}{125} \, x^{6} - \frac{51759}{3125} \, x^{5} - \frac{181521}{12500} \, x^{4} + \frac{2052}{3125} \, x^{3} + \frac{129654}{15625} \, x^{2} + \frac{1851147}{390625} \, x - \frac{458 \, x + 277}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{2037}{1953125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^7*(2*x - 1)/(5*x + 3)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212504, size = 97, normalized size = 1.33 \[ -\frac{1139062500 \, x^{8} + 4601812500 \, x^{7} + 7128253125 \, x^{6} + 4439846250 \, x^{5} - 753519375 \, x^{4} - 2916553500 \, x^{3} - 1694131200 \, x^{2} - 8148 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 333201880 \, x + 2770}{7812500 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^7*(2*x - 1)/(5*x + 3)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.30555, size = 63, normalized size = 0.86 \[ - \frac{729 x^{6}}{125} - \frac{51759 x^{5}}{3125} - \frac{181521 x^{4}}{12500} + \frac{2052 x^{3}}{3125} + \frac{129654 x^{2}}{15625} + \frac{1851147 x}{390625} - \frac{458 x + 277}{19531250 x^{2} + 23437500 x + 7031250} + \frac{2037 \log{\left (5 x + 3 \right )}}{1953125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)**7/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206884, size = 70, normalized size = 0.96 \[ -\frac{729}{125} \, x^{6} - \frac{51759}{3125} \, x^{5} - \frac{181521}{12500} \, x^{4} + \frac{2052}{3125} \, x^{3} + \frac{129654}{15625} \, x^{2} + \frac{1851147}{390625} \, x - \frac{458 \, x + 277}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{2037}{1953125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^7*(2*x - 1)/(5*x + 3)^3,x, algorithm="giac")
[Out]