Optimal. Leaf size=128 \[ \frac{23 (1-2 x)^{5/2}}{588 (3 x+2)^4}-\frac{(1-2 x)^{5/2}}{315 (3 x+2)^5}-\frac{4693 (1-2 x)^{3/2}}{15876 (3 x+2)^3}-\frac{4693 \sqrt{1-2 x}}{222264 (3 x+2)}+\frac{4693 \sqrt{1-2 x}}{31752 (3 x+2)^2}-\frac{4693 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{111132 \sqrt{21}} \]
[Out]
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Rubi [A] time = 0.138231, antiderivative size = 128, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 6, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{23 (1-2 x)^{5/2}}{588 (3 x+2)^4}-\frac{(1-2 x)^{5/2}}{315 (3 x+2)^5}-\frac{4693 (1-2 x)^{3/2}}{15876 (3 x+2)^3}-\frac{4693 \sqrt{1-2 x}}{222264 (3 x+2)}+\frac{4693 \sqrt{1-2 x}}{31752 (3 x+2)^2}-\frac{4693 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{111132 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^6,x]
[Out]
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Rubi in Sympy [A] time = 14.4003, size = 112, normalized size = 0.88 \[ \frac{23 \left (- 2 x + 1\right )^{\frac{5}{2}}}{588 \left (3 x + 2\right )^{4}} - \frac{\left (- 2 x + 1\right )^{\frac{5}{2}}}{315 \left (3 x + 2\right )^{5}} - \frac{4693 \left (- 2 x + 1\right )^{\frac{3}{2}}}{15876 \left (3 x + 2\right )^{3}} - \frac{4693 \sqrt{- 2 x + 1}}{222264 \left (3 x + 2\right )} + \frac{4693 \sqrt{- 2 x + 1}}{31752 \left (3 x + 2\right )^{2}} - \frac{4693 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{2333772} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(3/2)*(3+5*x)**2/(2+3*x)**6,x)
[Out]
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Mathematica [A] time = 0.122395, size = 68, normalized size = 0.53 \[ \frac{-\frac{21 \sqrt{1-2 x} \left (1900665 x^4-5801265 x^3-8540988 x^2-2143262 x+292028\right )}{(3 x+2)^5}-46930 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{23337720} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^(3/2)*(3 + 5*x)^2)/(2 + 3*x)^6,x]
[Out]
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Maple [A] time = 0.019, size = 75, normalized size = 0.6 \[ -3888\,{\frac{1}{ \left ( -4-6\,x \right ) ^{5}} \left ( -{\frac{4693\, \left ( 1-2\,x \right ) ^{9/2}}{5334336}}-{\frac{907\, \left ( 1-2\,x \right ) ^{7/2}}{489888}}+{\frac{6119\, \left ( 1-2\,x \right ) ^{5/2}}{229635}}-{\frac{32851\, \left ( 1-2\,x \right ) ^{3/2}}{629856}}+{\frac{32851\,\sqrt{1-2\,x}}{1259712}} \right ) }-{\frac{4693\,\sqrt{21}}{2333772}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^6,x)
[Out]
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Maxima [A] time = 1.5132, size = 173, normalized size = 1.35 \[ \frac{4693}{4667544} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) - \frac{1900665 \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + 3999870 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 57567552 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 112678930 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 56339465 \, \sqrt{-2 \, x + 1}}{555660 \,{\left (243 \,{\left (2 \, x - 1\right )}^{5} + 2835 \,{\left (2 \, x - 1\right )}^{4} + 13230 \,{\left (2 \, x - 1\right )}^{3} + 30870 \,{\left (2 \, x - 1\right )}^{2} + 72030 \, x - 19208\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(-2*x + 1)^(3/2)/(3*x + 2)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222669, size = 161, normalized size = 1.26 \[ -\frac{\sqrt{21}{\left (\sqrt{21}{\left (1900665 \, x^{4} - 5801265 \, x^{3} - 8540988 \, x^{2} - 2143262 \, x + 292028\right )} \sqrt{-2 \, x + 1} - 23465 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{23337720 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(-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)**2/(2+3*x)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.215296, size = 157, normalized size = 1.23 \[ \frac{4693}{4667544} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{1900665 \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - 3999870 \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - 57567552 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + 112678930 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 56339465 \, \sqrt{-2 \, x + 1}}{17781120 \,{\left (3 \, x + 2\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(-2*x + 1)^(3/2)/(3*x + 2)^6,x, algorithm="giac")
[Out]