Optimal. Leaf size=59 \[ -\frac{12083 x+11597}{162 \left (3 x^2+5 x+2\right )^2}+\frac{7 (20298 x+16651)}{162 \left (3 x^2+5 x+2\right )}-883 \log (x+1)+\frac{23825}{27} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.099492, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.16 \[ -\frac{12083 x+11597}{162 \left (3 x^2+5 x+2\right )^2}+\frac{7 (20298 x+16651)}{162 \left (3 x^2+5 x+2\right )}-883 \log (x+1)+\frac{23825}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 22.1285, size = 61, normalized size = 1.03 \[ - \frac{\left (2 x + 3\right )^{3} \left (139 x + 121\right )}{6 \left (3 x^{2} + 5 x + 2\right )^{2}} + \frac{\left (2 x + 3\right ) \left (12736 x + 11149\right )}{18 \left (3 x^{2} + 5 x + 2\right )} - 883 \log{\left (x + 1 \right )} + \frac{23825 \log{\left (3 x + 2 \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3+2*x)**4/(3*x**2+5*x+2)**3,x)
[Out]
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Mathematica [A] time = 0.0646151, size = 62, normalized size = 1.05 \[ \frac{1}{54} \left (47650 \log (-6 x-4)-\frac{3 \left (-47362 x^3-117789 x^2+15894 \left (3 x^2+5 x+2\right )^2 \log (-2 (x+1))-94986 x-24613\right )}{\left (3 x^2+5 x+2\right )^2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^3,x]
[Out]
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Maple [A] time = 0.016, size = 48, normalized size = 0.8 \[ -{\frac{10625}{54\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{15500}{54+81\,x}}+{\frac{23825\,\ln \left ( 2+3\,x \right ) }{27}}+3\, \left ( 1+x \right ) ^{-2}+101\, \left ( 1+x \right ) ^{-1}-883\,\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3+2*x)^4/(3*x^2+5*x+2)^3,x)
[Out]
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Maxima [A] time = 0.690656, size = 73, normalized size = 1.24 \[ \frac{47362 \, x^{3} + 117789 \, x^{2} + 94986 \, x + 24613}{18 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )}} + \frac{23825}{27} \, \log \left (3 \, x + 2\right ) - 883 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^4*(x - 5)/(3*x^2 + 5*x + 2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.261854, size = 126, normalized size = 2.14 \[ \frac{142086 \, x^{3} + 353367 \, x^{2} + 47650 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 47682 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )} \log \left (x + 1\right ) + 284958 \, x + 73839}{54 \,{\left (9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^4*(x - 5)/(3*x^2 + 5*x + 2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.510305, size = 51, normalized size = 0.86 \[ \frac{47362 x^{3} + 117789 x^{2} + 94986 x + 24613}{162 x^{4} + 540 x^{3} + 666 x^{2} + 360 x + 72} + \frac{23825 \log{\left (x + \frac{2}{3} \right )}}{27} - 883 \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3+2*x)**4/(3*x**2+5*x+2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.292497, size = 62, normalized size = 1.05 \[ \frac{47362 \, x^{3} + 117789 \, x^{2} + 94986 \, x + 24613}{18 \,{\left (3 \, x + 2\right )}^{2}{\left (x + 1\right )}^{2}} + \frac{23825}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - 883 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^4*(x - 5)/(3*x^2 + 5*x + 2)^3,x, algorithm="giac")
[Out]