Optimal. Leaf size=39 \[ \frac{407}{25 (5 x+3)}-\frac{121}{50 (5 x+3)^2}-49 \log (3 x+2)+49 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0497769, antiderivative size = 39, 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 \[ \frac{407}{25 (5 x+3)}-\frac{121}{50 (5 x+3)^2}-49 \log (3 x+2)+49 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 7.33747, size = 32, normalized size = 0.82 \[ - 49 \log{\left (3 x + 2 \right )} + 49 \log{\left (5 x + 3 \right )} + \frac{407}{25 \left (5 x + 3\right )} - \frac{121}{50 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2/(2+3*x)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0316882, size = 48, normalized size = 1.23 \[ \frac{4070 x-2450 (5 x+3)^2 \log (3 x+2)+2450 (5 x+3)^2 \log (-3 (5 x+3))+2321}{50 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^2/((2 + 3*x)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.013, size = 36, normalized size = 0.9 \[ -{\frac{121}{50\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{407}{75+125\,x}}-49\,\ln \left ( 2+3\,x \right ) +49\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2/(2+3*x)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.33957, size = 49, normalized size = 1.26 \[ \frac{11 \,{\left (370 \, x + 211\right )}}{50 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + 49 \, \log \left (5 \, x + 3\right ) - 49 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213683, size = 74, normalized size = 1.9 \[ \frac{2450 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 2450 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 4070 \, x + 2321}{50 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.360707, size = 31, normalized size = 0.79 \[ \frac{4070 x + 2321}{1250 x^{2} + 1500 x + 450} + 49 \log{\left (x + \frac{3}{5} \right )} - 49 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2/(2+3*x)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.208774, size = 45, normalized size = 1.15 \[ \frac{11 \,{\left (370 \, x + 211\right )}}{50 \,{\left (5 \, x + 3\right )}^{2}} + 49 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 49 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x - 1)^2/((5*x + 3)^3*(3*x + 2)),x, algorithm="giac")
[Out]