Optimal. Leaf size=59 \[ -\frac{2025 x^4}{32}-\frac{7245 x^3}{16}-\frac{54783 x^2}{32}-\frac{176055 x}{32}-\frac{381073}{64 (1-2 x)}+\frac{290521}{256 (1-2 x)^2}-\frac{832951}{128} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.0796966, antiderivative size = 59, 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 \[ -\frac{2025 x^4}{32}-\frac{7245 x^3}{16}-\frac{54783 x^2}{32}-\frac{176055 x}{32}-\frac{381073}{64 (1-2 x)}+\frac{290521}{256 (1-2 x)^2}-\frac{832951}{128} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{2025 x^{4}}{32} - \frac{7245 x^{3}}{16} - \frac{832951 \log{\left (- 2 x + 1 \right )}}{128} + \int \left (- \frac{176055}{32}\right )\, dx - \frac{54783 \int x\, dx}{16} - \frac{381073}{64 \left (- 2 x + 1\right )} + \frac{290521}{256 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)**2/(1-2*x)**3,x)
[Out]
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Mathematica [A] time = 0.031495, size = 56, normalized size = 0.95 \[ -\frac{129600 x^6+797760 x^5+2611152 x^4+7993248 x^3-17025300 x^2+3354020 x+3331804 (1-2 x)^2 \log (1-2 x)+808965}{512 (1-2 x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^3,x]
[Out]
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Maple [A] time = 0.008, size = 46, normalized size = 0.8 \[ -{\frac{2025\,{x}^{4}}{32}}-{\frac{7245\,{x}^{3}}{16}}-{\frac{54783\,{x}^{2}}{32}}-{\frac{176055\,x}{32}}+{\frac{290521}{256\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{381073}{-64+128\,x}}-{\frac{832951\,\ln \left ( -1+2\,x \right ) }{128}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)^2/(1-2*x)^3,x)
[Out]
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Maxima [A] time = 1.34236, size = 62, normalized size = 1.05 \[ -\frac{2025}{32} \, x^{4} - \frac{7245}{16} \, x^{3} - \frac{54783}{32} \, x^{2} - \frac{176055}{32} \, x + \frac{3773 \,{\left (808 \, x - 327\right )}}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{832951}{128} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^4/(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212103, size = 84, normalized size = 1.42 \[ -\frac{64800 \, x^{6} + 398880 \, x^{5} + 1305576 \, x^{4} + 3996624 \, x^{3} - 5195496 \, x^{2} + 1665902 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1640144 \, x + 1233771}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^4/(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.314095, size = 49, normalized size = 0.83 \[ - \frac{2025 x^{4}}{32} - \frac{7245 x^{3}}{16} - \frac{54783 x^{2}}{32} - \frac{176055 x}{32} + \frac{3048584 x - 1233771}{1024 x^{2} - 1024 x + 256} - \frac{832951 \log{\left (2 x - 1 \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**4*(3+5*x)**2/(1-2*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.206454, size = 57, normalized size = 0.97 \[ -\frac{2025}{32} \, x^{4} - \frac{7245}{16} \, x^{3} - \frac{54783}{32} \, x^{2} - \frac{176055}{32} \, x + \frac{3773 \,{\left (808 \, x - 327\right )}}{256 \,{\left (2 \, x - 1\right )}^{2}} - \frac{832951}{128} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(3*x + 2)^4/(2*x - 1)^3,x, algorithm="giac")
[Out]