Optimal. Leaf size=147 \[ -\frac{275 \sqrt{1-2 x} (5 x+3)^3}{9 (3 x+2)}+\frac{55 (1-2 x)^{3/2} (5 x+3)^3}{27 (3 x+2)^2}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{9 (3 x+2)^3}+\frac{1441}{27} \sqrt{1-2 x} (5 x+3)^2-\frac{22}{243} \sqrt{1-2 x} (1885 x+578)-\frac{41360 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{243 \sqrt{21}} \]
[Out]
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Rubi [A] time = 0.288188, antiderivative size = 147, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 7, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.292 \[ -\frac{275 \sqrt{1-2 x} (5 x+3)^3}{9 (3 x+2)}+\frac{55 (1-2 x)^{3/2} (5 x+3)^3}{27 (3 x+2)^2}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{9 (3 x+2)^3}+\frac{1441}{27} \sqrt{1-2 x} (5 x+3)^2-\frac{22}{243} \sqrt{1-2 x} (1885 x+578)-\frac{41360 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{243 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^4,x]
[Out]
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Rubi in Sympy [A] time = 21.0823, size = 117, normalized size = 0.8 \[ \frac{11 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (12600 x + 9180\right )}{23814 \left (3 x + 2\right )} - \frac{55 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (5 x + 3\right )^{2}}{189 \left (3 x + 2\right )^{2}} - \frac{\left (- 2 x + 1\right )^{\frac{5}{2}} \left (5 x + 3\right )^{3}}{9 \left (3 x + 2\right )^{3}} + \frac{41360 \left (- 2 x + 1\right )^{\frac{3}{2}}}{11907} + \frac{41360 \sqrt{- 2 x + 1}}{1701} - \frac{41360 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{5103} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(5/2)*(3+5*x)**3/(2+3*x)**4,x)
[Out]
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Mathematica [A] time = 0.136946, size = 73, normalized size = 0.5 \[ \frac{\frac{21 \sqrt{1-2 x} \left (16200 x^5-20700 x^4+87030 x^3+289719 x^2+229336 x+56141\right )}{(3 x+2)^3}-41360 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{5103} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^4,x]
[Out]
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Maple [A] time = 0.019, size = 84, normalized size = 0.6 \[{\frac{50}{81} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}}+{\frac{2050}{729} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}+{\frac{16570}{729}\sqrt{1-2\,x}}+{\frac{2}{27\, \left ( -4-6\,x \right ) ^{3}} \left ( -{\frac{4153}{3} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}}+{\frac{172130}{27} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{198205}{27}\sqrt{1-2\,x}} \right ) }-{\frac{41360\,\sqrt{21}}{5103}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4,x)
[Out]
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Maxima [A] time = 1.49995, size = 161, normalized size = 1.1 \[ \frac{50}{81} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{2050}{729} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{20680}{5103} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{16570}{729} \, \sqrt{-2 \, x + 1} + \frac{2 \,{\left (37377 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 172130 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 198205 \, \sqrt{-2 \, x + 1}\right )}}{729 \,{\left (27 \,{\left (2 \, x - 1\right )}^{3} + 189 \,{\left (2 \, x - 1\right )}^{2} + 882 \, x - 98\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(5/2)/(3*x + 2)^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211639, size = 140, normalized size = 0.95 \[ \frac{\sqrt{21}{\left (\sqrt{21}{\left (16200 \, x^{5} - 20700 \, x^{4} + 87030 \, x^{3} + 289719 \, x^{2} + 229336 \, x + 56141\right )} \sqrt{-2 \, x + 1} + 20680 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{5103 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(5/2)/(3*x + 2)^4,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)**(5/2)*(3+5*x)**3/(2+3*x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.220987, size = 159, normalized size = 1.08 \[ \frac{50}{81} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{2050}{729} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{20680}{5103} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{16570}{729} \, \sqrt{-2 \, x + 1} + \frac{37377 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 172130 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 198205 \, \sqrt{-2 \, x + 1}}{2916 \,{\left (3 \, x + 2\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(5/2)/(3*x + 2)^4,x, algorithm="giac")
[Out]