Optimal. Leaf size=86 \[ \frac{189375}{3 x+2}+\frac{125000}{5 x+3}+\frac{12675}{(3 x+2)^2}-\frac{6875}{2 (5 x+3)^2}+\frac{1020}{(3 x+2)^3}+\frac{309}{4 (3 x+2)^4}+\frac{21}{5 (3 x+2)^5}-1321875 \log (3 x+2)+1321875 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.105477, antiderivative size = 86, 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 \[ \frac{189375}{3 x+2}+\frac{125000}{5 x+3}+\frac{12675}{(3 x+2)^2}-\frac{6875}{2 (5 x+3)^2}+\frac{1020}{(3 x+2)^3}+\frac{309}{4 (3 x+2)^4}+\frac{21}{5 (3 x+2)^5}-1321875 \log (3 x+2)+1321875 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 13.3165, size = 76, normalized size = 0.88 \[ - 1321875 \log{\left (3 x + 2 \right )} + 1321875 \log{\left (5 x + 3 \right )} + \frac{125000}{5 x + 3} - \frac{6875}{2 \left (5 x + 3\right )^{2}} + \frac{189375}{3 x + 2} + \frac{12675}{\left (3 x + 2\right )^{2}} + \frac{1020}{\left (3 x + 2\right )^{3}} + \frac{309}{4 \left (3 x + 2\right )^{4}} + \frac{21}{5 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)/(2+3*x)**6/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0519051, size = 88, normalized size = 1.02 \[ \frac{189375}{3 x+2}+\frac{125000}{5 x+3}+\frac{12675}{(3 x+2)^2}-\frac{6875}{2 (5 x+3)^2}+\frac{1020}{(3 x+2)^3}+\frac{309}{4 (3 x+2)^4}+\frac{21}{5 (3 x+2)^5}-1321875 \log (3 x+2)+1321875 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)/((2 + 3*x)^6*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.015, size = 81, normalized size = 0.9 \[{\frac{21}{5\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{309}{4\, \left ( 2+3\,x \right ) ^{4}}}+1020\, \left ( 2+3\,x \right ) ^{-3}+12675\, \left ( 2+3\,x \right ) ^{-2}+189375\, \left ( 2+3\,x \right ) ^{-1}-{\frac{6875}{2\, \left ( 3+5\,x \right ) ^{2}}}+125000\, \left ( 3+5\,x \right ) ^{-1}-1321875\,\ln \left ( 2+3\,x \right ) +1321875\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)/(2+3*x)^6/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.32751, size = 116, normalized size = 1.35 \[ \frac{10707187500 \, x^{6} + 41758031250 \, x^{5} + 67828050000 \, x^{4} + 58733814375 \, x^{3} + 28595335800 \, x^{2} + 7421662135 \, x + 802214966}{20 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )}} + 1321875 \, \log \left (5 \, x + 3\right ) - 1321875 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)^6),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210943, size = 209, normalized size = 2.43 \[ \frac{10707187500 \, x^{6} + 41758031250 \, x^{5} + 67828050000 \, x^{4} + 58733814375 \, x^{3} + 28595335800 \, x^{2} + 26437500 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )} \log \left (5 \, x + 3\right ) - 26437500 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )} \log \left (3 \, x + 2\right ) + 7421662135 \, x + 802214966}{20 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)^6),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.607091, size = 82, normalized size = 0.95 \[ \frac{10707187500 x^{6} + 41758031250 x^{5} + 67828050000 x^{4} + 58733814375 x^{3} + 28595335800 x^{2} + 7421662135 x + 802214966}{121500 x^{7} + 550800 x^{6} + 1069740 x^{5} + 1153800 x^{4} + 746400 x^{3} + 289600 x^{2} + 62400 x + 5760} + 1321875 \log{\left (x + \frac{3}{5} \right )} - 1321875 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)/(2+3*x)**6/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.207164, size = 88, normalized size = 1.02 \[ \frac{10707187500 \, x^{6} + 41758031250 \, x^{5} + 67828050000 \, x^{4} + 58733814375 \, x^{3} + 28595335800 \, x^{2} + 7421662135 \, x + 802214966}{20 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{5}} + 1321875 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 1321875 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)^3*(3*x + 2)^6),x, algorithm="giac")
[Out]