Optimal. Leaf size=62 \[ \frac{1215 x^6}{8}+\frac{5103 x^5}{5}+\frac{210195 x^4}{64}+\frac{111501 x^3}{16}+\frac{1507977 x^2}{128}+\frac{661617 x}{32}+\frac{1294139}{256 (1-2 x)}+\frac{3916031}{256} \log (1-2 x) \]
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Rubi [A] time = 0.0755691, antiderivative size = 62, 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 \[ \frac{1215 x^6}{8}+\frac{5103 x^5}{5}+\frac{210195 x^4}{64}+\frac{111501 x^3}{16}+\frac{1507977 x^2}{128}+\frac{661617 x}{32}+\frac{1294139}{256 (1-2 x)}+\frac{3916031}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{1215 x^{6}}{8} + \frac{5103 x^{5}}{5} + \frac{210195 x^{4}}{64} + \frac{111501 x^{3}}{16} + \frac{3916031 \log{\left (- 2 x + 1 \right )}}{256} + \int \frac{661617}{32}\, dx + \frac{1507977 \int x\, dx}{64} + \frac{1294139}{256 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6*(3+5*x)/(1-2*x)**2,x)
[Out]
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Mathematica [A] time = 0.0226708, size = 59, normalized size = 0.95 \[ \frac{1555200 x^7+9673344 x^6+28405728 x^5+54545040 x^4+84957840 x^3+151398360 x^2-253249902 x+78320620 (2 x-1) \log (1-2 x)+47812811}{5120 (2 x-1)} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^2,x]
[Out]
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Maple [A] time = 0.011, size = 47, normalized size = 0.8 \[{\frac{1215\,{x}^{6}}{8}}+{\frac{5103\,{x}^{5}}{5}}+{\frac{210195\,{x}^{4}}{64}}+{\frac{111501\,{x}^{3}}{16}}+{\frac{1507977\,{x}^{2}}{128}}+{\frac{661617\,x}{32}}-{\frac{1294139}{-256+512\,x}}+{\frac{3916031\,\ln \left ( -1+2\,x \right ) }{256}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6*(3+5*x)/(1-2*x)^2,x)
[Out]
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Maxima [A] time = 1.33192, size = 62, normalized size = 1. \[ \frac{1215}{8} \, x^{6} + \frac{5103}{5} \, x^{5} + \frac{210195}{64} \, x^{4} + \frac{111501}{16} \, x^{3} + \frac{1507977}{128} \, x^{2} + \frac{661617}{32} \, x - \frac{1294139}{256 \,{\left (2 \, x - 1\right )}} + \frac{3916031}{256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205307, size = 77, normalized size = 1.24 \[ \frac{388800 \, x^{7} + 2418336 \, x^{6} + 7101432 \, x^{5} + 13636260 \, x^{4} + 21239460 \, x^{3} + 37849590 \, x^{2} + 19580155 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 26464680 \, x - 6470695}{1280 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.234184, size = 54, normalized size = 0.87 \[ \frac{1215 x^{6}}{8} + \frac{5103 x^{5}}{5} + \frac{210195 x^{4}}{64} + \frac{111501 x^{3}}{16} + \frac{1507977 x^{2}}{128} + \frac{661617 x}{32} + \frac{3916031 \log{\left (2 x - 1 \right )}}{256} - \frac{1294139}{512 x - 256} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**6*(3+5*x)/(1-2*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.208981, size = 113, normalized size = 1.82 \[ \frac{9}{5120} \,{\left (2 \, x - 1\right )}^{6}{\left (\frac{26244}{2 \, x - 1} + \frac{227745}{{\left (2 \, x - 1\right )}^{2}} + \frac{1171100}{{\left (2 \, x - 1\right )}^{3}} + \frac{4064550}{{\left (2 \, x - 1\right )}^{4}} + \frac{11284700}{{\left (2 \, x - 1\right )}^{5}} + 1350\right )} - \frac{1294139}{256 \,{\left (2 \, x - 1\right )}} - \frac{3916031}{256} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6/(2*x - 1)^2,x, algorithm="giac")
[Out]