Optimal. Leaf size=59 \[ \frac{243 x}{500}+\frac{16807}{10648 (1-2 x)}-\frac{169}{831875 (5 x+3)}-\frac{1}{151250 (5 x+3)^2}+\frac{36015 \log (1-2 x)}{29282}+\frac{11562 \log (5 x+3)}{9150625} \]
[Out]
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Rubi [A] time = 0.0689739, antiderivative size = 59, 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 \[ \frac{243 x}{500}+\frac{16807}{10648 (1-2 x)}-\frac{169}{831875 (5 x+3)}-\frac{1}{151250 (5 x+3)^2}+\frac{36015 \log (1-2 x)}{29282}+\frac{11562 \log (5 x+3)}{9150625} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{36015 \log{\left (- 2 x + 1 \right )}}{29282} + \frac{11562 \log{\left (5 x + 3 \right )}}{9150625} + \int \frac{243}{500}\, dx - \frac{169}{831875 \left (5 x + 3\right )} - \frac{1}{151250 \left (5 x + 3\right )^{2}} + \frac{16807}{10648 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**5/(1-2*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0756651, size = 55, normalized size = 0.93 \[ \frac{17788815 (2 x-1)+\frac{115548125}{1-2 x}-\frac{14872}{5 x+3}-\frac{484}{(5 x+3)^2}+90037500 \log (1-2 x)+92496 \log (10 x+6)}{73205000} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^5/((1 - 2*x)^2*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.014, size = 48, normalized size = 0.8 \[{\frac{243\,x}{500}}-{\frac{1}{151250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{169}{2495625+4159375\,x}}+{\frac{11562\,\ln \left ( 3+5\,x \right ) }{9150625}}-{\frac{16807}{-10648+21296\,x}}+{\frac{36015\,\ln \left ( -1+2\,x \right ) }{29282}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^5/(1-2*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.34962, size = 66, normalized size = 1.12 \[ \frac{243}{500} \, x - \frac{52524579 \, x^{2} + 63026538 \, x + 18907055}{1331000 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{11562}{9150625} \, \log \left (5 \, x + 3\right ) + \frac{36015}{29282} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214649, size = 115, normalized size = 1.95 \[ \frac{1778881500 \, x^{4} + 1245217050 \, x^{3} - 3315783405 \, x^{2} + 92496 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 90037500 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) - 3786658260 \, x - 1039888025}{73205000 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.466219, size = 49, normalized size = 0.83 \[ \frac{243 x}{500} - \frac{52524579 x^{2} + 63026538 x + 18907055}{66550000 x^{3} + 46585000 x^{2} - 15972000 x - 11979000} + \frac{36015 \log{\left (x - \frac{1}{2} \right )}}{29282} + \frac{11562 \log{\left (x + \frac{3}{5} \right )}}{9150625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**5/(1-2*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.210478, size = 112, normalized size = 1.9 \[ \frac{{\left (2 \, x - 1\right )}{\left (\frac{391367530}{2 \, x - 1} + \frac{430519419}{{\left (2 \, x - 1\right )}^{2}} + 88944075\right )}}{14641000 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} - \frac{16807}{10648 \,{\left (2 \, x - 1\right )}} - \frac{1539}{1250} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{11562}{9150625} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="giac")
[Out]