Optimal. Leaf size=51 \[ \frac{81 x^3}{20}+\frac{567 x^2}{25}+\frac{152793 x}{2000}+\frac{16807}{352 (1-2 x)}+\frac{156065 \log (1-2 x)}{1936}+\frac{\log (5 x+3)}{75625} \]
[Out]
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Rubi [A] time = 0.057939, antiderivative size = 51, 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 \[ \frac{81 x^3}{20}+\frac{567 x^2}{25}+\frac{152793 x}{2000}+\frac{16807}{352 (1-2 x)}+\frac{156065 \log (1-2 x)}{1936}+\frac{\log (5 x+3)}{75625} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{81 x^{3}}{20} + \frac{156065 \log{\left (- 2 x + 1 \right )}}{1936} + \frac{\log{\left (5 x + 3 \right )}}{75625} + \int \frac{152793}{2000}\, dx + \frac{1134 \int x\, dx}{25} + \frac{16807}{352 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**5/(1-2*x)**2/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0396734, size = 52, normalized size = 1.02 \[ \frac{81 x^3}{20}+\frac{567 x^2}{25}+\frac{152793 x}{2000}+\frac{16807}{352-704 x}+\frac{156065 \log (5-10 x)}{1936}+\frac{\log (5 x+3)}{75625}+\frac{385479}{10000} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.012, size = 40, normalized size = 0.8 \[{\frac{81\,{x}^{3}}{20}}+{\frac{567\,{x}^{2}}{25}}+{\frac{152793\,x}{2000}}+{\frac{\ln \left ( 3+5\,x \right ) }{75625}}-{\frac{16807}{-352+704\,x}}+{\frac{156065\,\ln \left ( -1+2\,x \right ) }{1936}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^5/(1-2*x)^2/(3+5*x),x)
[Out]
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Maxima [A] time = 1.36359, size = 53, normalized size = 1.04 \[ \frac{81}{20} \, x^{3} + \frac{567}{25} \, x^{2} + \frac{152793}{2000} \, x - \frac{16807}{352 \,{\left (2 \, x - 1\right )}} + \frac{1}{75625} \, \log \left (5 \, x + 3\right ) + \frac{156065}{1936} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212772, size = 74, normalized size = 1.45 \[ \frac{19602000 \, x^{4} + 99970200 \, x^{3} + 314873460 \, x^{2} + 32 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 195081250 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 184879530 \, x - 115548125}{2420000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.331591, size = 42, normalized size = 0.82 \[ \frac{81 x^{3}}{20} + \frac{567 x^{2}}{25} + \frac{152793 x}{2000} + \frac{156065 \log{\left (x - \frac{1}{2} \right )}}{1936} + \frac{\log{\left (x + \frac{3}{5} \right )}}{75625} - \frac{16807}{704 x - 352} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**5/(1-2*x)**2/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.212572, size = 97, normalized size = 1.9 \[ \frac{27}{4000} \,{\left (2 \, x - 1\right )}^{3}{\left (\frac{1065}{2 \, x - 1} + \frac{7564}{{\left (2 \, x - 1\right )}^{2}} + 75\right )} - \frac{16807}{352 \,{\left (2 \, x - 1\right )}} - \frac{806121}{10000} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{75625} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)*(2*x - 1)^2),x, algorithm="giac")
[Out]