Optimal. Leaf size=53 \[ -\frac{9}{7 (3 x+2)}-\frac{25}{11 (5 x+3)}-\frac{8 \log (1-2 x)}{5929}+\frac{648}{49} \log (3 x+2)-\frac{1600}{121} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0633557, antiderivative size = 53, 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 \[ -\frac{9}{7 (3 x+2)}-\frac{25}{11 (5 x+3)}-\frac{8 \log (1-2 x)}{5929}+\frac{648}{49} \log (3 x+2)-\frac{1600}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 8.73333, size = 42, normalized size = 0.79 \[ - \frac{8 \log{\left (- 2 x + 1 \right )}}{5929} + \frac{648 \log{\left (3 x + 2 \right )}}{49} - \frac{1600 \log{\left (5 x + 3 \right )}}{121} - \frac{25}{11 \left (5 x + 3\right )} - \frac{9}{7 \left (3 x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**2/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0394897, size = 47, normalized size = 0.89 \[ \frac{2 \left (-\frac{7623}{6 x+4}-\frac{13475}{10 x+6}-4 \log (1-2 x)+39204 \log (6 x+4)-39200 \log (10 x+6)\right )}{5929} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^2*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.016, size = 44, normalized size = 0.8 \[ -{\frac{25}{33+55\,x}}-{\frac{1600\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{9}{14+21\,x}}+{\frac{648\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{8\,\ln \left ( -1+2\,x \right ) }{5929}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^2/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.35516, size = 59, normalized size = 1.11 \[ -\frac{1020 \, x + 647}{77 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} - \frac{1600}{121} \, \log \left (5 \, x + 3\right ) + \frac{648}{49} \, \log \left (3 \, x + 2\right ) - \frac{8}{5929} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^2*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219123, size = 99, normalized size = 1.87 \[ -\frac{78400 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 78408 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 8 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (2 \, x - 1\right ) + 78540 \, x + 49819}{5929 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^2*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.501347, size = 44, normalized size = 0.83 \[ - \frac{1020 x + 647}{1155 x^{2} + 1463 x + 462} - \frac{8 \log{\left (x - \frac{1}{2} \right )}}{5929} - \frac{1600 \log{\left (x + \frac{3}{5} \right )}}{121} + \frac{648 \log{\left (x + \frac{2}{3} \right )}}{49} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**2/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.219194, size = 72, normalized size = 1.36 \[ -\frac{25}{11 \,{\left (5 \, x + 3\right )}} + \frac{135}{7 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}} + \frac{648}{49} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{8}{5929} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)^2*(3*x + 2)^2*(2*x - 1)),x, algorithm="giac")
[Out]