Optimal. Leaf size=113 \[ -\frac{\sqrt{1-2 x} (3 x+2)^4}{55 (5 x+3)}-\frac{78 \sqrt{1-2 x} (3 x+2)^3}{1925}-\frac{1668 \sqrt{1-2 x} (3 x+2)^2}{6875}-\frac{6 \sqrt{1-2 x} (19875 x+59708)}{34375}-\frac{332 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{34375 \sqrt{55}} \]
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Rubi [A] time = 0.224328, antiderivative size = 113, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ -\frac{\sqrt{1-2 x} (3 x+2)^4}{55 (5 x+3)}-\frac{78 \sqrt{1-2 x} (3 x+2)^3}{1925}-\frac{1668 \sqrt{1-2 x} (3 x+2)^2}{6875}-\frac{6 \sqrt{1-2 x} (19875 x+59708)}{34375}-\frac{332 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{34375 \sqrt{55}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 25.5487, size = 99, normalized size = 0.88 \[ - \frac{\sqrt{- 2 x + 1} \left (3 x + 2\right )^{4}}{55 \left (5 x + 3\right )} - \frac{78 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{3}}{1925} - \frac{1668 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{2}}{6875} - \frac{\sqrt{- 2 x + 1} \left (12521250 x + 37616040\right )}{3609375} - \frac{332 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{1890625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**5/(3+5*x)**2/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.112031, size = 68, normalized size = 0.6 \[ \frac{-\frac{55 \sqrt{1-2 x} \left (1670625 x^4+6994350 x^3+13532310 x^2+20175210 x+8527768\right )}{5 x+3}-2324 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{13234375} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^5/(Sqrt[1 - 2*x]*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.018, size = 72, normalized size = 0.6 \[{\frac{243}{1400} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}}-{\frac{8829}{5000} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}}+{\frac{35703}{5000} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{434043}{25000}\sqrt{1-2\,x}}+{\frac{2}{171875}\sqrt{1-2\,x} \left ( -{\frac{6}{5}}-2\,x \right ) ^{-1}}-{\frac{332\,\sqrt{55}}{1890625}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^5/(3+5*x)^2/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.51409, size = 120, normalized size = 1.06 \[ \frac{243}{1400} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{8829}{5000} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{35703}{5000} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{166}{1890625} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{434043}{25000} \, \sqrt{-2 \, x + 1} - \frac{\sqrt{-2 \, x + 1}}{34375 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^2*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.24125, size = 107, normalized size = 0.95 \[ -\frac{\sqrt{55}{\left (\sqrt{55}{\left (1670625 \, x^{4} + 6994350 \, x^{3} + 13532310 \, x^{2} + 20175210 \, x + 8527768\right )} \sqrt{-2 \, x + 1} - 1162 \,{\left (5 \, x + 3\right )} \log \left (\frac{\sqrt{55}{\left (5 \, x - 8\right )} + 55 \, \sqrt{-2 \, x + 1}}{5 \, x + 3}\right )\right )}}{13234375 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^2*sqrt(-2*x + 1)),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**5/(3+5*x)**2/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213421, size = 143, normalized size = 1.27 \[ -\frac{243}{1400} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{8829}{5000} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{35703}{5000} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{166}{1890625} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{434043}{25000} \, \sqrt{-2 \, x + 1} - \frac{\sqrt{-2 \, x + 1}}{34375 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^2*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]