Optimal. Leaf size=79 \[ -\frac{32805 x^{10}}{4}-\frac{256365 x^9}{4}-\frac{14907321 x^8}{64}-\frac{8399295 x^7}{16}-\frac{53031699 x^6}{64}-\frac{316246329 x^5}{320}-\frac{487203129 x^4}{512}-\frac{204901139 x^3}{256}-\frac{677093689 x^2}{1024}-\frac{695181625 x}{1024}-\frac{697540921 \log (1-2 x)}{2048} \]
[Out]
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Rubi [A] time = 0.0774624, antiderivative size = 79, 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 \[ -\frac{32805 x^{10}}{4}-\frac{256365 x^9}{4}-\frac{14907321 x^8}{64}-\frac{8399295 x^7}{16}-\frac{53031699 x^6}{64}-\frac{316246329 x^5}{320}-\frac{487203129 x^4}{512}-\frac{204901139 x^3}{256}-\frac{677093689 x^2}{1024}-\frac{695181625 x}{1024}-\frac{697540921 \log (1-2 x)}{2048} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{32805 x^{10}}{4} - \frac{256365 x^{9}}{4} - \frac{14907321 x^{8}}{64} - \frac{8399295 x^{7}}{16} - \frac{53031699 x^{6}}{64} - \frac{316246329 x^{5}}{320} - \frac{487203129 x^{4}}{512} - \frac{204901139 x^{3}}{256} - \frac{697540921 \log{\left (- 2 x + 1 \right )}}{2048} + \int \left (- \frac{695181625}{1024}\right )\, dx - \frac{677093689 \int x\, dx}{512} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**8*(3+5*x)**2/(1-2*x),x)
[Out]
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Mathematica [A] time = 0.0243641, size = 62, normalized size = 0.78 \[ \frac{-671846400 x^{10}-5250355200 x^9-19081370880 x^8-43004390400 x^7-67880574720 x^6-80959060224 x^5-77952500640 x^4-65568364480 x^3-54167495120 x^2-55614530000 x-27901636840 \log (1-2 x)+58429239347}{81920} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^8*(3 + 5*x)^2)/(1 - 2*x),x]
[Out]
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Maple [A] time = 0.004, size = 58, normalized size = 0.7 \[ -{\frac{32805\,{x}^{10}}{4}}-{\frac{256365\,{x}^{9}}{4}}-{\frac{14907321\,{x}^{8}}{64}}-{\frac{8399295\,{x}^{7}}{16}}-{\frac{53031699\,{x}^{6}}{64}}-{\frac{316246329\,{x}^{5}}{320}}-{\frac{487203129\,{x}^{4}}{512}}-{\frac{204901139\,{x}^{3}}{256}}-{\frac{677093689\,{x}^{2}}{1024}}-{\frac{695181625\,x}{1024}}-{\frac{697540921\,\ln \left ( -1+2\,x \right ) }{2048}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^8*(3+5*x)^2/(1-2*x),x)
[Out]
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Maxima [A] time = 1.34173, size = 77, normalized size = 0.97 \[ -\frac{32805}{4} \, x^{10} - \frac{256365}{4} \, x^{9} - \frac{14907321}{64} \, x^{8} - \frac{8399295}{16} \, x^{7} - \frac{53031699}{64} \, x^{6} - \frac{316246329}{320} \, x^{5} - \frac{487203129}{512} \, x^{4} - \frac{204901139}{256} \, x^{3} - \frac{677093689}{1024} \, x^{2} - \frac{695181625}{1024} \, x - \frac{697540921}{2048} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^8/(2*x - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220771, size = 77, normalized size = 0.97 \[ -\frac{32805}{4} \, x^{10} - \frac{256365}{4} \, x^{9} - \frac{14907321}{64} \, x^{8} - \frac{8399295}{16} \, x^{7} - \frac{53031699}{64} \, x^{6} - \frac{316246329}{320} \, x^{5} - \frac{487203129}{512} \, x^{4} - \frac{204901139}{256} \, x^{3} - \frac{677093689}{1024} \, x^{2} - \frac{695181625}{1024} \, x - \frac{697540921}{2048} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^8/(2*x - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.250122, size = 76, normalized size = 0.96 \[ - \frac{32805 x^{10}}{4} - \frac{256365 x^{9}}{4} - \frac{14907321 x^{8}}{64} - \frac{8399295 x^{7}}{16} - \frac{53031699 x^{6}}{64} - \frac{316246329 x^{5}}{320} - \frac{487203129 x^{4}}{512} - \frac{204901139 x^{3}}{256} - \frac{677093689 x^{2}}{1024} - \frac{695181625 x}{1024} - \frac{697540921 \log{\left (2 x - 1 \right )}}{2048} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**8*(3+5*x)**2/(1-2*x),x)
[Out]
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GIAC/XCAS [A] time = 0.207131, size = 78, normalized size = 0.99 \[ -\frac{32805}{4} \, x^{10} - \frac{256365}{4} \, x^{9} - \frac{14907321}{64} \, x^{8} - \frac{8399295}{16} \, x^{7} - \frac{53031699}{64} \, x^{6} - \frac{316246329}{320} \, x^{5} - \frac{487203129}{512} \, x^{4} - \frac{204901139}{256} \, x^{3} - \frac{677093689}{1024} \, x^{2} - \frac{695181625}{1024} \, x - \frac{697540921}{2048} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^8/(2*x - 1),x, algorithm="giac")
[Out]