Optimal. Leaf size=37 \[ \frac{11}{3 x+2}+\frac{7}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0443608, 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 \[ \frac{11}{3 x+2}+\frac{7}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 6.68312, size = 32, normalized size = 0.86 \[ - 55 \log{\left (3 x + 2 \right )} + 55 \log{\left (5 x + 3 \right )} + \frac{11}{3 x + 2} + \frac{7}{6 \left (3 x + 2\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)/(2+3*x)**3/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0523764, size = 35, normalized size = 0.95 \[ \frac{198 x+139}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)/((2 + 3*x)^3*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.01, size = 36, normalized size = 1. \[{\frac{7}{6\, \left ( 2+3\,x \right ) ^{2}}}+11\, \left ( 2+3\,x \right ) ^{-1}-55\,\ln \left ( 2+3\,x \right ) +55\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)/(2+3*x)^3/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34826, size = 49, normalized size = 1.32 \[ \frac{198 \, x + 139}{6 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + 55 \, \log \left (5 \, x + 3\right ) - 55 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215653, size = 74, normalized size = 2. \[ \frac{330 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 330 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 198 \, x + 139}{6 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.305841, size = 31, normalized size = 0.84 \[ \frac{198 x + 139}{54 x^{2} + 72 x + 24} + 55 \log{\left (x + \frac{3}{5} \right )} - 55 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)/(2+3*x)**3/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.212718, size = 45, normalized size = 1.22 \[ \frac{198 \, x + 139}{6 \,{\left (3 \, x + 2\right )}^{2}} + 55 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 55 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^3),x, algorithm="giac")
[Out]