Optimal. Leaf size=44 \[ -\frac{81 x^2}{100}-\frac{1593 x}{500}-\frac{1}{6875 (5 x+3)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (5 x+3)}{75625} \]
[Out]
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Rubi [A] time = 0.0511634, antiderivative size = 44, 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 \[ -\frac{81 x^2}{100}-\frac{1593 x}{500}-\frac{1}{6875 (5 x+3)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (5 x+3)}{75625} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{2401 \log{\left (- 2 x + 1 \right )}}{968} + \frac{134 \log{\left (5 x + 3 \right )}}{75625} + \int \left (- \frac{1593}{500}\right )\, dx - \frac{81 \int x\, dx}{50} - \frac{1}{6875 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4/(1-2*x)/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0422189, size = 52, normalized size = 1.18 \[ -\frac{81}{400} (1-2 x)^2+\frac{999}{500} (1-2 x)-\frac{1}{6875 (5 x+3)}-\frac{2401}{968} \log (1-2 x)+\frac{134 \log (10 x+6)}{75625} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.011, size = 35, normalized size = 0.8 \[ -{\frac{81\,{x}^{2}}{100}}-{\frac{1593\,x}{500}}-{\frac{1}{20625+34375\,x}}+{\frac{134\,\ln \left ( 3+5\,x \right ) }{75625}}-{\frac{2401\,\ln \left ( -1+2\,x \right ) }{968}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4/(1-2*x)/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.35532, size = 46, normalized size = 1.05 \[ -\frac{81}{100} \, x^{2} - \frac{1593}{500} \, x - \frac{1}{6875 \,{\left (5 \, x + 3\right )}} + \frac{134}{75625} \, \log \left (5 \, x + 3\right ) - \frac{2401}{968} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4/((5*x + 3)^2*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209155, size = 68, normalized size = 1.55 \[ -\frac{2450250 \, x^{3} + 11107800 \, x^{2} - 1072 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 1500625 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 5782590 \, x + 88}{605000 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4/((5*x + 3)^2*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.356241, size = 37, normalized size = 0.84 \[ - \frac{81 x^{2}}{100} - \frac{1593 x}{500} - \frac{2401 \log{\left (x - \frac{1}{2} \right )}}{968} + \frac{134 \log{\left (x + \frac{3}{5} \right )}}{75625} - \frac{1}{34375 x + 20625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**4/(1-2*x)/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.207017, size = 85, normalized size = 1.93 \[ -\frac{27}{2500} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{41}{5 \, x + 3} + 3\right )} - \frac{1}{6875 \,{\left (5 \, x + 3\right )}} + \frac{12393}{5000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{2401}{968} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4/((5*x + 3)^2*(2*x - 1)),x, algorithm="giac")
[Out]