Optimal. Leaf size=100 \[ \frac{7 (3 x+2)^2}{33 (1-2 x)^{3/2} (5 x+3)^2}+\frac{17296 x+10217}{39930 \sqrt{1-2 x} (5 x+3)^2}-\frac{7559 \sqrt{1-2 x}}{146410 (5 x+3)}-\frac{7559 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{73205 \sqrt{55}} \]
[Out]
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Rubi [A] time = 0.136685, antiderivative size = 100, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ \frac{7 (3 x+2)^2}{33 (1-2 x)^{3/2} (5 x+3)^2}+\frac{17296 x+10217}{39930 \sqrt{1-2 x} (5 x+3)^2}-\frac{7559 \sqrt{1-2 x}}{146410 (5 x+3)}-\frac{7559 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{73205 \sqrt{55}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 13.8433, size = 87, normalized size = 0.87 \[ - \frac{7559 \sqrt{- 2 x + 1}}{146410 \left (5 x + 3\right )} - \frac{7559 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{4026275} + \frac{17296 x + 10217}{39930 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{2}} + \frac{7 \left (3 x + 2\right )^{2}}{33 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3/(1-2*x)**(5/2)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.121823, size = 66, normalized size = 0.66 \[ \frac{-\frac{55 \sqrt{1-2 x} \left (453540 x^3-639434 x^2-1242261 x-417036\right )}{\left (10 x^2+x-3\right )^2}-45354 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{24157650} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^3/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.022, size = 66, normalized size = 0.7 \[{\frac{343}{3993} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}}+{\frac{294}{14641}{\frac{1}{\sqrt{1-2\,x}}}}+{\frac{50}{14641\, \left ( -6-10\,x \right ) ^{2}} \left ({\frac{209}{50} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{2321}{250}\sqrt{1-2\,x}} \right ) }-{\frac{7559\,\sqrt{55}}{4026275}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3/(1-2*x)^(5/2)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.49465, size = 124, normalized size = 1.24 \[ \frac{7559}{8052550} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{113385 \,{\left (2 \, x - 1\right )}^{3} + 20438 \,{\left (2 \, x - 1\right )}^{2} - 3083080 \, x - 741125}{219615 \,{\left (25 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 110 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 121 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^3*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222287, size = 136, normalized size = 1.36 \[ \frac{\sqrt{55}{\left (22677 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \sqrt{-2 \, x + 1} \log \left (\frac{\sqrt{55}{\left (5 \, x - 8\right )} + 55 \, \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) + \sqrt{55}{\left (453540 \, x^{3} - 639434 \, x^{2} - 1242261 \, x - 417036\right )}\right )}}{24157650 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^3*(-2*x + 1)^(5/2)),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)**3/(1-2*x)**(5/2)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.22761, size = 120, normalized size = 1.2 \[ \frac{7559}{8052550} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{49 \,{\left (36 \, x - 95\right )}}{43923 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} + \frac{95 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 211 \, \sqrt{-2 \, x + 1}}{26620 \,{\left (5 \, x + 3\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^3*(-2*x + 1)^(5/2)),x, algorithm="giac")
[Out]