Optimal. Leaf size=64 \[ \frac{502254 x+398585}{486 \left (3 x^2+5 x+2\right )}-\frac{57499 x+56041}{486 \left (3 x^2+5 x+2\right )^2}-\frac{32 x}{27}-1085 \log (x+1)+\frac{29375}{27} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.141617, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 5, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{502254 x+398585}{486 \left (3 x^2+5 x+2\right )}-\frac{57499 x+56041}{486 \left (3 x^2+5 x+2\right )^2}-\frac{32 x}{27}-1085 \log (x+1)+\frac{29375}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(3 + 2*x)^5)/(2 + 5*x + 3*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 28.6883, size = 68, normalized size = 1.06 \[ - \frac{7780 x}{9} - \frac{\left (2 x + 3\right )^{4} \left (139 x + 121\right )}{6 \left (3 x^{2} + 5 x + 2\right )^{2}} + \frac{\left (2 x + 3\right )^{2} \left (12210 x + 10515\right )}{18 \left (3 x^{2} + 5 x + 2\right )} - 1085 \log{\left (x + 1 \right )} + \frac{29375 \log{\left (3 x + 2 \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3+2*x)**5/(3*x**2+5*x+2)**3,x)
[Out]
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Mathematica [A] time = 0.061183, size = 81, normalized size = 1.27 \[ \frac{-1728 x^5-8352 x^4+486510 x^3+1221179 x^2+176250 \left (3 x^2+5 x+2\right )^2 \log (-6 x-4)-175770 \left (3 x^2+5 x+2\right )^2 \log (-2 (x+1))+973450 x+245891}{162 \left (3 x^2+5 x+2\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(3 + 2*x)^5)/(2 + 5*x + 3*x^2)^3,x]
[Out]
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Maple [A] time = 0.016, size = 51, normalized size = 0.8 \[ -{\frac{32\,x}{27}}-{\frac{53125}{162\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{6250}{18+27\,x}}+{\frac{29375\,\ln \left ( 2+3\,x \right ) }{27}}+3\, \left ( 1+x \right ) ^{-2}+113\, \left ( 1+x \right ) ^{-1}-1085\,\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3+2*x)^5/(3*x^2+5*x+2)^3,x)
[Out]
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Maxima [A] time = 0.688255, size = 77, normalized size = 1.2 \[ -\frac{32}{27} \, x + \frac{502254 \, x^{3} + 1235675 \, x^{2} + 979978 \, x + 247043}{162 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )}} + \frac{29375}{27} \, \log \left (3 \, x + 2\right ) - 1085 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^5*(x - 5)/(3*x^2 + 5*x + 2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.261693, size = 139, normalized size = 2.17 \[ -\frac{1728 \, x^{5} + 5760 \, x^{4} - 495150 \, x^{3} - 1231835 \, x^{2} - 176250 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 175770 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )} \log \left (x + 1\right ) - 979210 \, x - 247043}{162 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^5*(x - 5)/(3*x^2 + 5*x + 2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.527669, size = 56, normalized size = 0.88 \[ - \frac{32 x}{27} + \frac{502254 x^{3} + 1235675 x^{2} + 979978 x + 247043}{1458 x^{4} + 4860 x^{3} + 5994 x^{2} + 3240 x + 648} + \frac{29375 \log{\left (x + \frac{2}{3} \right )}}{27} - 1085 \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3+2*x)**5/(3*x**2+5*x+2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.265084, size = 66, normalized size = 1.03 \[ -\frac{32}{27} \, x + \frac{502254 \, x^{3} + 1235675 \, x^{2} + 979978 \, x + 247043}{162 \,{\left (3 \, x + 2\right )}^{2}{\left (x + 1\right )}^{2}} + \frac{29375}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - 1085 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^5*(x - 5)/(3*x^2 + 5*x + 2)^3,x, algorithm="giac")
[Out]