Optimal. Leaf size=80 \[ -\frac{32805 x^7}{56}-\frac{162567 x^6}{32}-\frac{213597 x^5}{10}-\frac{7568235 x^4}{128}-\frac{16042509 x^3}{128}-\frac{118841283 x^2}{512}-\frac{120864213 x}{256}-\frac{246239357}{1024 (1-2 x)}+\frac{63412811}{2048 (1-2 x)^2}-\frac{106237047}{256} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.100743, antiderivative size = 80, 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 \[ -\frac{32805 x^7}{56}-\frac{162567 x^6}{32}-\frac{213597 x^5}{10}-\frac{7568235 x^4}{128}-\frac{16042509 x^3}{128}-\frac{118841283 x^2}{512}-\frac{120864213 x}{256}-\frac{246239357}{1024 (1-2 x)}+\frac{63412811}{2048 (1-2 x)^2}-\frac{106237047}{256} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{32805 x^{7}}{56} - \frac{162567 x^{6}}{32} - \frac{213597 x^{5}}{10} - \frac{7568235 x^{4}}{128} - \frac{16042509 x^{3}}{128} - \frac{106237047 \log{\left (- 2 x + 1 \right )}}{256} + \int \left (- \frac{120864213}{256}\right )\, dx - \frac{118841283 \int x\, dx}{256} - \frac{246239357}{1024 \left (- 2 x + 1\right )} + \frac{63412811}{2048 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**8*(3+5*x)/(1-2*x)**3,x)
[Out]
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Mathematica [A] time = 0.0350548, size = 71, normalized size = 0.89 \[ -\frac{83980800 x^9+644319360 x^8+2354821632 x^7+5596371648 x^6+10256718528 x^5+17427054960 x^4+38900302560 x^3-104409393876 x^2+44728559236 x+14873186580 (1-2 x)^2 \log (1-2 x)-3752427799}{35840 (1-2 x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^8*(3 + 5*x))/(1 - 2*x)^3,x]
[Out]
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Maple [A] time = 0.012, size = 61, normalized size = 0.8 \[ -{\frac{32805\,{x}^{7}}{56}}-{\frac{162567\,{x}^{6}}{32}}-{\frac{213597\,{x}^{5}}{10}}-{\frac{7568235\,{x}^{4}}{128}}-{\frac{16042509\,{x}^{3}}{128}}-{\frac{118841283\,{x}^{2}}{512}}-{\frac{120864213\,x}{256}}+{\frac{63412811}{2048\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{246239357}{-1024+2048\,x}}-{\frac{106237047\,\ln \left ( -1+2\,x \right ) }{256}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^8*(3+5*x)/(1-2*x)^3,x)
[Out]
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Maxima [A] time = 1.34523, size = 82, normalized size = 1.02 \[ -\frac{32805}{56} \, x^{7} - \frac{162567}{32} \, x^{6} - \frac{213597}{10} \, x^{5} - \frac{7568235}{128} \, x^{4} - \frac{16042509}{128} \, x^{3} - \frac{118841283}{512} \, x^{2} - \frac{120864213}{256} \, x + \frac{823543 \,{\left (1196 \, x - 521\right )}}{2048 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{106237047}{256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(3*x + 2)^8/(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2068, size = 104, normalized size = 1.3 \[ -\frac{167961600 \, x^{9} + 1288638720 \, x^{8} + 4709643264 \, x^{7} + 11192743296 \, x^{6} + 20513437056 \, x^{5} + 34854109920 \, x^{4} + 77800605120 \, x^{3} - 118730138940 \, x^{2} + 29746373160 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 631530340 \, x + 15017306605}{71680 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(3*x + 2)^8/(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.331483, size = 70, normalized size = 0.88 \[ - \frac{32805 x^{7}}{56} - \frac{162567 x^{6}}{32} - \frac{213597 x^{5}}{10} - \frac{7568235 x^{4}}{128} - \frac{16042509 x^{3}}{128} - \frac{118841283 x^{2}}{512} - \frac{120864213 x}{256} + \frac{984957428 x - 429065903}{8192 x^{2} - 8192 x + 2048} - \frac{106237047 \log{\left (2 x - 1 \right )}}{256} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**8*(3+5*x)/(1-2*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.210714, size = 77, normalized size = 0.96 \[ -\frac{32805}{56} \, x^{7} - \frac{162567}{32} \, x^{6} - \frac{213597}{10} \, x^{5} - \frac{7568235}{128} \, x^{4} - \frac{16042509}{128} \, x^{3} - \frac{118841283}{512} \, x^{2} - \frac{120864213}{256} \, x + \frac{823543 \,{\left (1196 \, x - 521\right )}}{2048 \,{\left (2 \, x - 1\right )}^{2}} - \frac{106237047}{256} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(3*x + 2)^8/(2*x - 1)^3,x, algorithm="giac")
[Out]