Optimal. Leaf size=120 \[ \frac{\sqrt{1-2 x} (5 x+3)^2}{105 (3 x+2)^5}+\frac{\sqrt{1-2 x} (1971 x+1255)}{6615 (3 x+2)^4}-\frac{5293 \sqrt{1-2 x}}{43218 (3 x+2)}-\frac{5293 \sqrt{1-2 x}}{18522 (3 x+2)^2}-\frac{5293 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{21609 \sqrt{21}} \]
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Rubi [A] time = 0.151539, antiderivative size = 120, 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 \[ \frac{\sqrt{1-2 x} (5 x+3)^2}{105 (3 x+2)^5}+\frac{\sqrt{1-2 x} (1971 x+1255)}{6615 (3 x+2)^4}-\frac{5293 \sqrt{1-2 x}}{43218 (3 x+2)}-\frac{5293 \sqrt{1-2 x}}{18522 (3 x+2)^2}-\frac{5293 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{21609 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]
[Out]
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Rubi in Sympy [A] time = 15.7059, size = 104, normalized size = 0.87 \[ - \frac{5293 \sqrt{- 2 x + 1}}{43218 \left (3 x + 2\right )} - \frac{5293 \sqrt{- 2 x + 1}}{18522 \left (3 x + 2\right )^{2}} + \frac{\sqrt{- 2 x + 1} \left (165564 x + 105420\right )}{555660 \left (3 x + 2\right )^{4}} + \frac{\sqrt{- 2 x + 1} \left (5 x + 3\right )^{2}}{105 \left (3 x + 2\right )^{5}} - \frac{5293 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{453789} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(2+3*x)**6/(1-2*x)**(1/2),x)
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Mathematica [A] time = 0.136995, size = 68, normalized size = 0.57 \[ \frac{-\frac{21 \sqrt{1-2 x} \left (2143665 x^4+7383735 x^3+8806422 x^2+4450198 x+816938\right )}{(3 x+2)^5}-52930 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{4537890} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/(Sqrt[1 - 2*x]*(2 + 3*x)^6),x]
[Out]
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Maple [A] time = 0.017, size = 75, normalized size = 0.6 \[ 1944\,{\frac{1}{ \left ( -4-6\,x \right ) ^{5}} \left ({\frac{5293\, \left ( 1-2\,x \right ) ^{9/2}}{518616}}-{\frac{5293\, \left ( 1-2\,x \right ) ^{7/2}}{47628}}+{\frac{78563\, \left ( 1-2\,x \right ) ^{5/2}}{178605}}-{\frac{324347\, \left ( 1-2\,x \right ) ^{3/2}}{428652}}+{\frac{58781\,\sqrt{1-2\,x}}{122472}} \right ) }-{\frac{5293\,\sqrt{21}}{453789}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(2+3*x)^6/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.51553, size = 173, normalized size = 1.44 \[ \frac{5293}{907578} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) - \frac{2143665 \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - 23342130 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + 92390088 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 158930030 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 100809415 \, \sqrt{-2 \, x + 1}}{108045 \,{\left (243 \,{\left (2 \, x - 1\right )}^{5} + 2835 \,{\left (2 \, x - 1\right )}^{4} + 13230 \,{\left (2 \, x - 1\right )}^{3} + 30870 \,{\left (2 \, x - 1\right )}^{2} + 72030 \, x - 19208\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^6*sqrt(-2*x + 1)),x, algorithm="maxima")
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Fricas [A] time = 0.250714, size = 161, normalized size = 1.34 \[ -\frac{\sqrt{21}{\left (\sqrt{21}{\left (2143665 \, x^{4} + 7383735 \, x^{3} + 8806422 \, x^{2} + 4450198 \, x + 816938\right )} \sqrt{-2 \, x + 1} - 26465 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{4537890 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^6*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((3+5*x)**3/(2+3*x)**6/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.219115, size = 157, normalized size = 1.31 \[ \frac{5293}{907578} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{2143665 \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + 23342130 \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + 92390088 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 158930030 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 100809415 \, \sqrt{-2 \, x + 1}}{3457440 \,{\left (3 \, x + 2\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^6*sqrt(-2*x + 1)),x, algorithm="giac")
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