Optimal. Leaf size=46 \[ \frac{21}{3 x+2}+\frac{68}{5 x+3}-\frac{11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0546662, antiderivative size = 46, 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 \[ \frac{21}{3 x+2}+\frac{68}{5 x+3}-\frac{11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 7.93288, size = 39, normalized size = 0.85 \[ - 309 \log{\left (3 x + 2 \right )} + 309 \log{\left (5 x + 3 \right )} + \frac{68}{5 x + 3} - \frac{11}{2 \left (5 x + 3\right )^{2}} + \frac{21}{3 x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)/(2+3*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0298167, size = 48, normalized size = 1.04 \[ \frac{21}{3 x+2}+\frac{68}{5 x+3}-\frac{11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)/((2 + 3*x)^2*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.014, size = 45, normalized size = 1. \[ 21\, \left ( 2+3\,x \right ) ^{-1}-{\frac{11}{2\, \left ( 3+5\,x \right ) ^{2}}}+68\, \left ( 3+5\,x \right ) ^{-1}-309\,\ln \left ( 2+3\,x \right ) +309\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)/(2+3*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.32709, size = 62, normalized size = 1.35 \[ \frac{3090 \, x^{2} + 3811 \, x + 1172}{2 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 309 \, \log \left (5 \, x + 3\right ) - 309 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210728, size = 101, normalized size = 2.2 \[ \frac{3090 \, x^{2} + 618 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 618 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 3811 \, x + 1172}{2 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.356907, size = 41, normalized size = 0.89 \[ \frac{3090 x^{2} + 3811 x + 1172}{150 x^{3} + 280 x^{2} + 174 x + 36} + 309 \log{\left (x + \frac{3}{5} \right )} - 309 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)/(2+3*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.209807, size = 66, normalized size = 1.43 \[ \frac{21}{3 \, x + 2} - \frac{15 \,{\left (\frac{202}{3 \, x + 2} - 845\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + 309 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="giac")
[Out]