Optimal. Leaf size=59 \[ -\frac{1215 x^4}{32}-\frac{4401 x^3}{16}-\frac{16821 x^2}{16}-\frac{109089 x}{32}-\frac{60025}{16 (1-2 x)}+\frac{184877}{256 (1-2 x)^2}-\frac{519645}{128} \log (1-2 x) \]
[Out]
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Rubi [A] time = 0.0741948, antiderivative size = 59, 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 \[ -\frac{1215 x^4}{32}-\frac{4401 x^3}{16}-\frac{16821 x^2}{16}-\frac{109089 x}{32}-\frac{60025}{16 (1-2 x)}+\frac{184877}{256 (1-2 x)^2}-\frac{519645}{128} \log (1-2 x) \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{1215 x^{4}}{32} - \frac{4401 x^{3}}{16} - \frac{519645 \log{\left (- 2 x + 1 \right )}}{128} + \int \left (- \frac{109089}{32}\right )\, dx - \frac{16821 \int x\, dx}{8} - \frac{60025}{16 \left (- 2 x + 1\right )} + \frac{184877}{256 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**5*(3+5*x)/(1-2*x)**3,x)
[Out]
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Mathematica [A] time = 0.0282951, size = 56, normalized size = 0.95 \[ -\frac{77760 x^6+485568 x^5+1609200 x^4+4969440 x^3-10547820 x^2+2008220 x+2078580 (1-2 x)^2 \log (1-2 x)+524947}{512 (1-2 x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^5*(3 + 5*x))/(1 - 2*x)^3,x]
[Out]
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Maple [A] time = 0.01, size = 46, normalized size = 0.8 \[ -{\frac{1215\,{x}^{4}}{32}}-{\frac{4401\,{x}^{3}}{16}}-{\frac{16821\,{x}^{2}}{16}}-{\frac{109089\,x}{32}}+{\frac{184877}{256\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{60025}{-16+32\,x}}-{\frac{519645\,\ln \left ( -1+2\,x \right ) }{128}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^5*(3+5*x)/(1-2*x)^3,x)
[Out]
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Maxima [A] time = 1.34429, size = 62, normalized size = 1.05 \[ -\frac{1215}{32} \, x^{4} - \frac{4401}{16} \, x^{3} - \frac{16821}{16} \, x^{2} - \frac{109089}{32} \, x + \frac{2401 \,{\left (800 \, x - 323\right )}}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{519645}{128} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(3*x + 2)^5/(2*x - 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219981, size = 84, normalized size = 1.42 \[ -\frac{38880 \, x^{6} + 242784 \, x^{5} + 804600 \, x^{4} + 2484720 \, x^{3} - 3221712 \, x^{2} + 1039290 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1048088 \, x + 775523}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(3*x + 2)^5/(2*x - 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.298809, size = 49, normalized size = 0.83 \[ - \frac{1215 x^{4}}{32} - \frac{4401 x^{3}}{16} - \frac{16821 x^{2}}{16} - \frac{109089 x}{32} + \frac{1920800 x - 775523}{1024 x^{2} - 1024 x + 256} - \frac{519645 \log{\left (2 x - 1 \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**5*(3+5*x)/(1-2*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.211941, size = 57, normalized size = 0.97 \[ -\frac{1215}{32} \, x^{4} - \frac{4401}{16} \, x^{3} - \frac{16821}{16} \, x^{2} - \frac{109089}{32} \, x + \frac{2401 \,{\left (800 \, x - 323\right )}}{256 \,{\left (2 \, x - 1\right )}^{2}} - \frac{519645}{128} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(3*x + 2)^5/(2*x - 1)^3,x, algorithm="giac")
[Out]