Optimal. Leaf size=68 \[ \frac{6934}{3 x+2}+\frac{7480}{5 x+3}+\frac{707}{2 (3 x+2)^2}-\frac{605}{2 (5 x+3)^2}+\frac{49}{3 (3 x+2)^3}-57110 \log (3 x+2)+57110 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0839258, antiderivative size = 68, 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 \[ \frac{6934}{3 x+2}+\frac{7480}{5 x+3}+\frac{707}{2 (3 x+2)^2}-\frac{605}{2 (5 x+3)^2}+\frac{49}{3 (3 x+2)^3}-57110 \log (3 x+2)+57110 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 10.8955, size = 60, normalized size = 0.88 \[ - 57110 \log{\left (3 x + 2 \right )} + 57110 \log{\left (5 x + 3 \right )} + \frac{7480}{5 x + 3} - \frac{605}{2 \left (5 x + 3\right )^{2}} + \frac{6934}{3 x + 2} + \frac{707}{2 \left (3 x + 2\right )^{2}} + \frac{49}{3 \left (3 x + 2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)**4/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0783331, size = 70, normalized size = 1.03 \[ \frac{6934}{3 x+2}+\frac{7480}{5 x+3}+\frac{707}{2 (3 x+2)^2}-\frac{605}{2 (5 x+3)^2}+\frac{49}{3 (3 x+2)^3}-57110 \log (5 (3 x+2))+57110 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)^4*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.014, size = 63, normalized size = 0.9 \[{\frac{49}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{707}{2\, \left ( 2+3\,x \right ) ^{2}}}+6934\, \left ( 2+3\,x \right ) ^{-1}-{\frac{605}{2\, \left ( 3+5\,x \right ) ^{2}}}+7480\, \left ( 3+5\,x \right ) ^{-1}-57110\,\ln \left ( 2+3\,x \right ) +57110\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)^4/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.32786, size = 89, normalized size = 1.31 \[ \frac{15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 16250079 \, x + 2599404}{6 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + 57110 \, \log \left (5 \, x + 3\right ) - 57110 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217762, size = 155, normalized size = 2.28 \[ \frac{15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 342660 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 342660 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) + 16250079 \, x + 2599404}{6 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.490149, size = 61, normalized size = 0.9 \[ \frac{15419700 x^{4} + 39577230 x^{3} + 38058104 x^{2} + 16250079 x + 2599404}{4050 x^{5} + 12960 x^{4} + 16578 x^{3} + 10596 x^{2} + 3384 x + 432} + 57110 \log{\left (x + \frac{3}{5} \right )} - 57110 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)**4/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.207062, size = 74, normalized size = 1.09 \[ \frac{15419700 \, x^{4} + 39577230 \, x^{3} + 38058104 \, x^{2} + 16250079 \, x + 2599404}{6 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{3}} + 57110 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 57110 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)^4),x, algorithm="giac")
[Out]