Optimal. Leaf size=50 \[ \frac{7189}{27 (3 x+2)}+\frac{1421}{54 (3 x+2)^2}+\frac{343}{81 (3 x+2)^3}-1331 \log (3 x+2)+1331 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0566312, antiderivative size = 50, 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 \[ \frac{7189}{27 (3 x+2)}+\frac{1421}{54 (3 x+2)^2}+\frac{343}{81 (3 x+2)^3}-1331 \log (3 x+2)+1331 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 8.42503, size = 42, normalized size = 0.84 \[ - 1331 \log{\left (3 x + 2 \right )} + 1331 \log{\left (5 x + 3 \right )} + \frac{7189}{27 \left (3 x + 2\right )} + \frac{1421}{54 \left (3 x + 2\right )^{2}} + \frac{343}{81 \left (3 x + 2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3/(2+3*x)**4/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0450027, size = 40, normalized size = 0.8 \[ \frac{7 \left (55458 x^2+75771 x+25964\right )}{162 (3 x+2)^3}-1331 \log (5 (3 x+2))+1331 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3/((2 + 3*x)^4*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.011, size = 45, normalized size = 0.9 \[{\frac{343}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1421}{54\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{7189}{54+81\,x}}-1331\,\ln \left ( 2+3\,x \right ) +1331\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3/(2+3*x)^4/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34679, size = 62, normalized size = 1.24 \[ \frac{7 \,{\left (55458 \, x^{2} + 75771 \, x + 25964\right )}}{162 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + 1331 \, \log \left (5 \, x + 3\right ) - 1331 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21747, size = 101, normalized size = 2.02 \[ \frac{388206 \, x^{2} + 215622 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 215622 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 530397 \, x + 181748}{162 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.42678, size = 41, normalized size = 0.82 \[ \frac{388206 x^{2} + 530397 x + 181748}{4374 x^{3} + 8748 x^{2} + 5832 x + 1296} + 1331 \log{\left (x + \frac{3}{5} \right )} - 1331 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3/(2+3*x)**4/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.212659, size = 51, normalized size = 1.02 \[ \frac{7 \,{\left (55458 \, x^{2} + 75771 \, x + 25964\right )}}{162 \,{\left (3 \, x + 2\right )}^{3}} + 1331 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 1331 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^4),x, algorithm="giac")
[Out]