Optimal. Leaf size=81 \[ \frac{6875}{3 x+2}+\frac{1375}{2 (3 x+2)^2}+\frac{275}{3 (3 x+2)^3}+\frac{55}{4 (3 x+2)^4}+\frac{11}{5 (3 x+2)^5}+\frac{7}{18 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (5 x+3) \]
[Out]
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Rubi [A] time = 0.0746975, antiderivative size = 81, 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 \[ \frac{6875}{3 x+2}+\frac{1375}{2 (3 x+2)^2}+\frac{275}{3 (3 x+2)^3}+\frac{55}{4 (3 x+2)^4}+\frac{11}{5 (3 x+2)^5}+\frac{7}{18 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (5 x+3) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)/((2 + 3*x)^7*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [A] time = 11.1584, size = 73, normalized size = 0.9 \[ - 34375 \log{\left (3 x + 2 \right )} + 34375 \log{\left (5 x + 3 \right )} + \frac{6875}{3 x + 2} + \frac{1375}{2 \left (3 x + 2\right )^{2}} + \frac{275}{3 \left (3 x + 2\right )^{3}} + \frac{55}{4 \left (3 x + 2\right )^{4}} + \frac{11}{5 \left (3 x + 2\right )^{5}} + \frac{7}{18 \left (3 x + 2\right )^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)/(2+3*x)**7/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0744008, size = 75, normalized size = 0.93 \[ \frac{1237500 (3 x+2)^5+123750 (3 x+2)^4+16500 (3 x+2)^3+2475 (3 x+2)^2+396 (3 x+2)+70}{180 (3 x+2)^6}-34375 \log (3 x+2)+34375 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)/((2 + 3*x)^7*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.012, size = 72, normalized size = 0.9 \[{\frac{7}{18\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{11}{5\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{55}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{275}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1375}{2\, \left ( 2+3\,x \right ) ^{2}}}+6875\, \left ( 2+3\,x \right ) ^{-1}-34375\,\ln \left ( 2+3\,x \right ) +34375\,\ln \left ( 3+5\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)/(2+3*x)^7/(3+5*x),x)
[Out]
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Maxima [A] time = 1.35008, size = 103, normalized size = 1.27 \[ \frac{300712500 \, x^{5} + 1012398750 \, x^{4} + 1363675500 \, x^{3} + 918643275 \, x^{2} + 309504888 \, x + 41722762}{180 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 34375 \, \log \left (5 \, x + 3\right ) - 34375 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208175, size = 182, normalized size = 2.25 \[ \frac{300712500 \, x^{5} + 1012398750 \, x^{4} + 1363675500 \, x^{3} + 918643275 \, x^{2} + 6187500 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 6187500 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 309504888 \, x + 41722762}{180 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.505178, size = 71, normalized size = 0.88 \[ \frac{300712500 x^{5} + 1012398750 x^{4} + 1363675500 x^{3} + 918643275 x^{2} + 309504888 x + 41722762}{131220 x^{6} + 524880 x^{5} + 874800 x^{4} + 777600 x^{3} + 388800 x^{2} + 103680 x + 11520} + 34375 \log{\left (x + \frac{3}{5} \right )} - 34375 \log{\left (x + \frac{2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)/(2+3*x)**7/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.211074, size = 72, normalized size = 0.89 \[ \frac{300712500 \, x^{5} + 1012398750 \, x^{4} + 1363675500 \, x^{3} + 918643275 \, x^{2} + 309504888 \, x + 41722762}{180 \,{\left (3 \, x + 2\right )}^{6}} + 34375 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 34375 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x - 1)/((5*x + 3)*(3*x + 2)^7),x, algorithm="giac")
[Out]