Optimal. Leaf size=76 \[ \frac{388}{16807 (1-2 x)}-\frac{558}{16807 (3 x+2)}+\frac{22}{2401 (1-2 x)^2}-\frac{87}{4802 (3 x+2)^2}+\frac{1}{343 (3 x+2)^3}-\frac{2280 \log (1-2 x)}{117649}+\frac{2280 \log (3 x+2)}{117649} \]
[Out]
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Rubi [A] time = 0.0824247, antiderivative size = 76, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{388}{16807 (1-2 x)}-\frac{558}{16807 (3 x+2)}+\frac{22}{2401 (1-2 x)^2}-\frac{87}{4802 (3 x+2)^2}+\frac{1}{343 (3 x+2)^3}-\frac{2280 \log (1-2 x)}{117649}+\frac{2280 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^4),x]
[Out]
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Rubi in Sympy [A] time = 11.1818, size = 63, normalized size = 0.83 \[ - \frac{2280 \log{\left (- 2 x + 1 \right )}}{117649} + \frac{2280 \log{\left (3 x + 2 \right )}}{117649} - \frac{558}{16807 \left (3 x + 2\right )} - \frac{87}{4802 \left (3 x + 2\right )^{2}} + \frac{1}{343 \left (3 x + 2\right )^{3}} + \frac{388}{16807 \left (- 2 x + 1\right )} + \frac{22}{2401 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(1-2*x)**3/(2+3*x)**4,x)
[Out]
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Mathematica [A] time = 0.0575851, size = 57, normalized size = 0.75 \[ \frac{-\frac{7 \left (82080 x^4+75240 x^3-31160 x^2-33725 x-3088\right )}{(1-2 x)^2 (3 x+2)^3}-4560 \log (3-6 x)+4560 \log (3 x+2)}{235298} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/((1 - 2*x)^3*(2 + 3*x)^4),x]
[Out]
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Maple [A] time = 0.015, size = 63, normalized size = 0.8 \[{\frac{1}{343\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{87}{4802\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{558}{33614+50421\,x}}+{\frac{2280\,\ln \left ( 2+3\,x \right ) }{117649}}+{\frac{22}{2401\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{388}{-16807+33614\,x}}-{\frac{2280\,\ln \left ( -1+2\,x \right ) }{117649}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(1-2*x)^3/(2+3*x)^4,x)
[Out]
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Maxima [A] time = 1.35141, size = 89, normalized size = 1.17 \[ -\frac{82080 \, x^{4} + 75240 \, x^{3} - 31160 \, x^{2} - 33725 \, x - 3088}{33614 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac{2280}{117649} \, \log \left (3 \, x + 2\right ) - \frac{2280}{117649} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217054, size = 155, normalized size = 2.04 \[ -\frac{574560 \, x^{4} + 526680 \, x^{3} - 218120 \, x^{2} - 4560 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 4560 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 236075 \, x - 21616}{235298 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.479341, size = 65, normalized size = 0.86 \[ - \frac{82080 x^{4} + 75240 x^{3} - 31160 x^{2} - 33725 x - 3088}{3630312 x^{5} + 3630312 x^{4} - 1512630 x^{3} - 1949612 x^{2} + 134456 x + 268912} - \frac{2280 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{2280 \log{\left (x + \frac{2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)/(1-2*x)**3/(2+3*x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.209794, size = 74, normalized size = 0.97 \[ -\frac{82080 \, x^{4} + 75240 \, x^{3} - 31160 \, x^{2} - 33725 \, x - 3088}{33614 \,{\left (3 \, x + 2\right )}^{3}{\left (2 \, x - 1\right )}^{2}} + \frac{2280}{117649} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{2280}{117649} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="giac")
[Out]