Optimal. Leaf size=64 \[ \frac{3897}{343 (3 x+2)}+\frac{111}{98 (3 x+2)^2}+\frac{1}{7 (3 x+2)^3}-\frac{16 \log (1-2 x)}{26411}-\frac{136419 \log (3 x+2)}{2401}+\frac{625}{11} \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0710004, antiderivative size = 64, 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 \[ \frac{3897}{343 (3 x+2)}+\frac{111}{98 (3 x+2)^2}+\frac{1}{7 (3 x+2)^3}-\frac{16 \log (1-2 x)}{26411}-\frac{136419 \log (3 x+2)}{2401}+\frac{625}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 10.0042, size = 56, normalized size = 0.88 \[ - \frac{16 \log{\left (- 2 x + 1 \right )}}{26411} - \frac{136419 \log{\left (3 x + 2 \right )}}{2401} + \frac{625 \log{\left (5 x + 3 \right )}}{11} + \frac{3897}{343 \left (3 x + 2\right )} + \frac{111}{98 \left (3 x + 2\right )^{2}} + \frac{1}{7 \left (3 x + 2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)/(2+3*x)**4/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0799657, size = 50, normalized size = 0.78 \[ \frac{\frac{77 \left (70146 x^2+95859 x+32828\right )}{2 (3 x+2)^3}-16 \log (1-2 x)-1500609 \log (6 x+4)+1500625 \log (10 x+6)}{26411} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.014, size = 53, normalized size = 0.8 \[{\frac{625\,\ln \left ( 3+5\,x \right ) }{11}}+{\frac{1}{7\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{111}{98\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{3897}{686+1029\,x}}-{\frac{136419\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{16\,\ln \left ( -1+2\,x \right ) }{26411}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)/(2+3*x)^4/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34475, size = 73, normalized size = 1.14 \[ \frac{70146 \, x^{2} + 95859 \, x + 32828}{686 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{625}{11} \, \log \left (5 \, x + 3\right ) - \frac{136419}{2401} \, \log \left (3 \, x + 2\right ) - \frac{16}{26411} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220139, size = 132, normalized size = 2.06 \[ \frac{5401242 \, x^{2} + 3001250 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 3001218 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 32 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 7381143 \, x + 2527756}{52822 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.555386, size = 54, normalized size = 0.84 \[ \frac{70146 x^{2} + 95859 x + 32828}{18522 x^{3} + 37044 x^{2} + 24696 x + 5488} - \frac{16 \log{\left (x - \frac{1}{2} \right )}}{26411} + \frac{625 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{136419 \log{\left (x + \frac{2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)/(2+3*x)**4/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.215064, size = 63, normalized size = 0.98 \[ \frac{70146 \, x^{2} + 95859 \, x + 32828}{686 \,{\left (3 \, x + 2\right )}^{3}} + \frac{625}{11} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{136419}{2401} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{16}{26411} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)),x, algorithm="giac")
[Out]