Optimal. Leaf size=37 \[ \frac{7}{5 x+3}-\frac{11}{10 (5 x+3)^2}-21 \log (3 x+2)+21 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.044964, antiderivative size = 37, 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 \[ \frac{7}{5 x+3}-\frac{11}{10 (5 x+3)^2}-21 \log (3 x+2)+21 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 6.80705, size = 32, normalized size = 0.86 \[ - 21 \log{\left (3 x + 2 \right )} + 21 \log{\left (5 x + 3 \right )} + \frac{7}{5 x + 3} - \frac{11}{10 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)/(2+3*x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0214494, size = 48, normalized size = 1.3 \[ \frac{350 x-210 (5 x+3)^2 \log (5 (3 x+2))+210 (5 x+3)^2 \log (5 x+3)+199}{10 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)/((2 + 3*x)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.012, size = 36, normalized size = 1. \[ -{\frac{11}{10\, \left ( 3+5\,x \right ) ^{2}}}+7\, \left ( 3+5\,x \right ) ^{-1}-21\,\ln \left ( 2+3\,x \right ) +21\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)/(2+3*x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.38461, size = 49, normalized size = 1.32 \[ \frac{350 \, x + 199}{10 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + 21 \, \log \left (5 \, x + 3\right ) - 21 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219873, size = 74, normalized size = 2. \[ \frac{210 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 210 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 350 \, x + 199}{10 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.306998, size = 31, normalized size = 0.84 \[ \frac{350 x + 199}{250 x^{2} + 300 x + 90} + 21 \log{\left (x + \frac{3}{5} \right )} - 21 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)/(2+3*x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206365, size = 45, normalized size = 1.22 \[ \frac{350 \, x + 199}{10 \,{\left (5 \, x + 3\right )}^{2}} + 21 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 21 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)),x, algorithm="giac")
[Out]