Optimal. Leaf size=134 \[ \frac{3 \sqrt{1-2 x} (5 x+3)^3}{5 (3 x+2)^4}-\frac{(1-2 x)^{3/2} (5 x+3)^3}{15 (3 x+2)^5}-\frac{67 \sqrt{1-2 x} (5 x+3)^2}{315 (3 x+2)^3}-\frac{2 \sqrt{1-2 x} (15074 x+9529)}{9261 (3 x+2)^2}-\frac{13892 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{9261 \sqrt{21}} \]
[Out]
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Rubi [A] time = 0.209828, antiderivative size = 134, 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 \[ \frac{3 \sqrt{1-2 x} (5 x+3)^3}{5 (3 x+2)^4}-\frac{(1-2 x)^{3/2} (5 x+3)^3}{15 (3 x+2)^5}-\frac{67 \sqrt{1-2 x} (5 x+3)^2}{315 (3 x+2)^3}-\frac{2 \sqrt{1-2 x} (15074 x+9529)}{9261 (3 x+2)^2}-\frac{13892 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{9261 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^6,x]
[Out]
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Rubi in Sympy [A] time = 22.4241, size = 110, normalized size = 0.82 \[ - \frac{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (2896560 x + 1815120\right )}{3333960 \left (3 x + 2\right )^{3}} - \frac{3 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{2}}{35 \left (3 x + 2\right )^{4}} - \frac{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{3}}{15 \left (3 x + 2\right )^{5}} + \frac{6946 \sqrt{- 2 x + 1}}{9261 \left (3 x + 2\right )} - \frac{13892 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{194481} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(3/2)*(3+5*x)**3/(2+3*x)**6,x)
[Out]
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Mathematica [A] time = 0.127583, size = 68, normalized size = 0.51 \[ \frac{\frac{63 \sqrt{1-2 x} \left (4904370 x^4+10375830 x^3+7992771 x^2+2619854 x+300049\right )}{(3 x+2)^5}-208380 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{2917215} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^3)/(2 + 3*x)^6,x]
[Out]
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Maple [A] time = 0.017, size = 75, normalized size = 0.6 \[ 1944\,{\frac{1}{ \left ( -4-6\,x \right ) ^{5}} \left ( -{\frac{54493\, \left ( 1-2\,x \right ) ^{9/2}}{500094}}+{\frac{4577\, \left ( 1-2\,x \right ) ^{7/2}}{5103}}-{\frac{210293\, \left ( 1-2\,x \right ) ^{5/2}}{76545}}+{\frac{24311\, \left ( 1-2\,x \right ) ^{3/2}}{6561}}-{\frac{24311\,\sqrt{1-2\,x}}{13122}} \right ) }-{\frac{13892\,\sqrt{21}}{194481}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6,x)
[Out]
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Maxima [A] time = 1.5039, size = 173, normalized size = 1.29 \[ \frac{6946}{194481} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{4 \,{\left (2452185 \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - 20184570 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + 61826142 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 83386730 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 41693365 \, \sqrt{-2 \, x + 1}\right )}}{46305 \,{\left (243 \,{\left (2 \, x - 1\right )}^{5} + 2835 \,{\left (2 \, x - 1\right )}^{4} + 13230 \,{\left (2 \, x - 1\right )}^{3} + 30870 \,{\left (2 \, x - 1\right )}^{2} + 72030 \, x - 19208\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(3/2)/(3*x + 2)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210318, size = 161, normalized size = 1.2 \[ \frac{\sqrt{21}{\left (\sqrt{21}{\left (4904370 \, x^{4} + 10375830 \, x^{3} + 7992771 \, x^{2} + 2619854 \, x + 300049\right )} \sqrt{-2 \, x + 1} + 34730 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{972405 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(3/2)/(3*x + 2)^6,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(3/2)*(3+5*x)**3/(2+3*x)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.216499, size = 157, normalized size = 1.17 \[ \frac{6946}{194481} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{2452185 \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + 20184570 \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + 61826142 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 83386730 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 41693365 \, \sqrt{-2 \, x + 1}}{370440 \,{\left (3 \, x + 2\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(3/2)/(3*x + 2)^6,x, algorithm="giac")
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