Optimal. Leaf size=92 \[ \frac{75625}{3 x+2}+\frac{15125}{2 (3 x+2)^2}+\frac{3025}{3 (3 x+2)^3}+\frac{605}{4 (3 x+2)^4}+\frac{121}{5 (3 x+2)^5}+\frac{217}{54 (3 x+2)^6}+\frac{7}{9 (3 x+2)^7}-378125 \log (3 x+2)+378125 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0922425, antiderivative size = 92, 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 \[ \frac{75625}{3 x+2}+\frac{15125}{2 (3 x+2)^2}+\frac{3025}{3 (3 x+2)^3}+\frac{605}{4 (3 x+2)^4}+\frac{121}{5 (3 x+2)^5}+\frac{217}{54 (3 x+2)^6}+\frac{7}{9 (3 x+2)^7}-378125 \log (3 x+2)+378125 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 13.0541, size = 83, normalized size = 0.9 \[ - 378125 \log{\left (3 x + 2 \right )} + 378125 \log{\left (5 x + 3 \right )} + \frac{75625}{3 x + 2} + \frac{15125}{2 \left (3 x + 2\right )^{2}} + \frac{3025}{3 \left (3 x + 2\right )^{3}} + \frac{605}{4 \left (3 x + 2\right )^{4}} + \frac{121}{5 \left (3 x + 2\right )^{5}} + \frac{217}{54 \left (3 x + 2\right )^{6}} + \frac{7}{9 \left (3 x + 2\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**8/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.107101, size = 84, normalized size = 0.91 \[ \frac{40837500 (3 x+2)^6+4083750 (3 x+2)^5+544500 (3 x+2)^4+81675 (3 x+2)^3+13068 (3 x+2)^2+2170 (3 x+2)+420}{540 (3 x+2)^7}-378125 \log (5 (3 x+2))+378125 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^8*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.018, size = 81, normalized size = 0.9 \[{\frac{7}{9\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{217}{54\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{121}{5\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{605}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{3025}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{15125}{2\, \left ( 2+3\,x \right ) ^{2}}}+75625\, \left ( 2+3\,x \right ) ^{-1}-378125\,\ln \left ( 2+3\,x \right ) +378125\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^8/(3+5*x),x)
[Out]
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Maxima [A] time = 1.3528, size = 116, normalized size = 1.26 \[ \frac{29770537500 \, x^{6} + 120074501250 \, x^{5} + 201822192000 \, x^{4} + 180948267225 \, x^{3} + 91271440062 \, x^{2} + 24557875626 \, x + 2753702432}{540 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + 378125 \, \log \left (5 \, x + 3\right ) - 378125 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^8),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201523, size = 209, normalized size = 2.27 \[ \frac{29770537500 \, x^{6} + 120074501250 \, x^{5} + 201822192000 \, x^{4} + 180948267225 \, x^{3} + 91271440062 \, x^{2} + 204187500 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (5 \, x + 3\right ) - 204187500 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (3 \, x + 2\right ) + 24557875626 \, x + 2753702432}{540 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^8),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.604274, size = 82, normalized size = 0.89 \[ \frac{29770537500 x^{6} + 120074501250 x^{5} + 201822192000 x^{4} + 180948267225 x^{3} + 91271440062 x^{2} + 24557875626 x + 2753702432}{1180980 x^{7} + 5511240 x^{6} + 11022480 x^{5} + 12247200 x^{4} + 8164800 x^{3} + 3265920 x^{2} + 725760 x + 69120} + 378125 \log{\left (x + \frac{3}{5} \right )} - 378125 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**8/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.207199, size = 78, normalized size = 0.85 \[ \frac{29770537500 \, x^{6} + 120074501250 \, x^{5} + 201822192000 \, x^{4} + 180948267225 \, x^{3} + 91271440062 \, x^{2} + 24557875626 \, x + 2753702432}{540 \,{\left (3 \, x + 2\right )}^{7}} + 378125 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 378125 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)*(3*x + 2)^8),x, algorithm="giac")
[Out]