Optimal. Leaf size=92 \[ \frac{166375}{3 x+2}+\frac{33275}{2 (3 x+2)^2}+\frac{6655}{3 (3 x+2)^3}+\frac{1331}{4 (3 x+2)^4}+\frac{7189}{135 (3 x+2)^5}+\frac{1421}{162 (3 x+2)^6}+\frac{49}{27 (3 x+2)^7}-831875 \log (3 x+2)+831875 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.091703, antiderivative size = 92, 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 \[ \frac{166375}{3 x+2}+\frac{33275}{2 (3 x+2)^2}+\frac{6655}{3 (3 x+2)^3}+\frac{1331}{4 (3 x+2)^4}+\frac{7189}{135 (3 x+2)^5}+\frac{1421}{162 (3 x+2)^6}+\frac{49}{27 (3 x+2)^7}-831875 \log (3 x+2)+831875 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 6.49426, size = 83, normalized size = 0.9 \[ - 831875 \log{\left (3 x + 2 \right )} + 831875 \log{\left (5 x + 3 \right )} + \frac{166375}{3 x + 2} + \frac{33275}{2 \left (3 x + 2\right )^{2}} + \frac{6655}{3 \left (3 x + 2\right )^{3}} + \frac{1331}{4 \left (3 x + 2\right )^{4}} + \frac{7189}{135 \left (3 x + 2\right )^{5}} + \frac{1421}{162 \left (3 x + 2\right )^{6}} + \frac{49}{27 \left (3 x + 2\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3/(2+3*x)**8/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.110612, size = 84, normalized size = 0.91 \[ \frac{269527500 (3 x+2)^6+26952750 (3 x+2)^5+3593700 (3 x+2)^4+539055 (3 x+2)^3+86268 (3 x+2)^2+14210 (3 x+2)+2940}{1620 (3 x+2)^7}-831875 \log (5 (3 x+2))+831875 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^3/((2 + 3*x)^8*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.015, size = 81, normalized size = 0.9 \[{\frac{49}{27\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{1421}{162\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{7189}{135\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{1331}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{6655}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{33275}{2\, \left ( 2+3\,x \right ) ^{2}}}+166375\, \left ( 2+3\,x \right ) ^{-1}-831875\,\ln \left ( 2+3\,x \right ) +831875\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3/(2+3*x)^8/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34951, size = 116, normalized size = 1.26 \[ \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 162081979026 \, x + 18174436072}{1620 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + 831875 \, \log \left (5 \, x + 3\right ) - 831875 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^8),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219927, size = 209, normalized size = 2.27 \[ \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 1347637500 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (5 \, x + 3\right ) - 1347637500 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (3 \, x + 2\right ) + 162081979026 \, x + 18174436072}{1620 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^8),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.609661, size = 82, normalized size = 0.89 \[ \frac{196485547500 x^{6} + 792491708250 x^{5} + 1332026467200 x^{4} + 1194258563685 x^{3} + 602391504582 x^{2} + 162081979026 x + 18174436072}{3542940 x^{7} + 16533720 x^{6} + 33067440 x^{5} + 36741600 x^{4} + 24494400 x^{3} + 9797760 x^{2} + 2177280 x + 207360} + 831875 \log{\left (x + \frac{3}{5} \right )} - 831875 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3/(2+3*x)**8/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.2124, size = 78, normalized size = 0.85 \[ \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 162081979026 \, x + 18174436072}{1620 \,{\left (3 \, x + 2\right )}^{7}} + 831875 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 831875 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)^3/((5*x + 3)*(3*x + 2)^8),x, algorithm="giac")
[Out]