Optimal. Leaf size=42 \[ \frac{3}{7 (3 x+2)}-\frac{4}{539} \log (1-2 x)-\frac{111}{49} \log (3 x+2)+\frac{25}{11} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.050652, antiderivative size = 42, 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 \[ \frac{3}{7 (3 x+2)}-\frac{4}{539} \log (1-2 x)-\frac{111}{49} \log (3 x+2)+\frac{25}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 7.49406, size = 36, normalized size = 0.86 \[ - \frac{4 \log{\left (- 2 x + 1 \right )}}{539} - \frac{111 \log{\left (3 x + 2 \right )}}{49} + \frac{25 \log{\left (5 x + 3 \right )}}{11} + \frac{3}{7 \left (3 x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**2/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0328795, size = 38, normalized size = 0.9 \[ \frac{1}{539} \left (\frac{231}{3 x+2}-4 \log (1-2 x)-1221 \log (6 x+4)+1225 \log (10 x+6)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.013, size = 35, normalized size = 0.8 \[{\frac{25\,\ln \left ( 3+5\,x \right ) }{11}}+{\frac{3}{14+21\,x}}-{\frac{111\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{4\,\ln \left ( -1+2\,x \right ) }{539}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^2/(3+5*x),x)
[Out]
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Maxima [A] time = 1.343, size = 46, normalized size = 1.1 \[ \frac{3}{7 \,{\left (3 \, x + 2\right )}} + \frac{25}{11} \, \log \left (5 \, x + 3\right ) - \frac{111}{49} \, \log \left (3 \, x + 2\right ) - \frac{4}{539} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^2*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220606, size = 68, normalized size = 1.62 \[ \frac{1225 \,{\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 1221 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 4 \,{\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 231}{539 \,{\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^2*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.413513, size = 36, normalized size = 0.86 \[ - \frac{4 \log{\left (x - \frac{1}{2} \right )}}{539} + \frac{25 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{111 \log{\left (x + \frac{2}{3} \right )}}{49} + \frac{3}{21 x + 14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**2/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.209265, size = 54, normalized size = 1.29 \[ \frac{3}{7 \,{\left (3 \, x + 2\right )}} + \frac{25}{11} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{4}{539} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^2*(2*x - 1)),x, algorithm="giac")
[Out]