Optimal. Leaf size=88 \[ -\frac{2245 \sqrt{1-2 x}}{6174 (3 x+2)}+\frac{205 \sqrt{1-2 x}}{2646 (3 x+2)^2}-\frac{\sqrt{1-2 x}}{189 (3 x+2)^3}-\frac{2245 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{3087 \sqrt{21}} \]
[Out]
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Rubi [A] time = 0.108727, antiderivative size = 88, 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 \[ -\frac{2245 \sqrt{1-2 x}}{6174 (3 x+2)}+\frac{205 \sqrt{1-2 x}}{2646 (3 x+2)^2}-\frac{\sqrt{1-2 x}}{189 (3 x+2)^3}-\frac{2245 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{3087 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]
[Out]
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Rubi in Sympy [A] time = 10.1461, size = 75, normalized size = 0.85 \[ - \frac{2245 \sqrt{- 2 x + 1}}{6174 \left (3 x + 2\right )} + \frac{205 \sqrt{- 2 x + 1}}{2646 \left (3 x + 2\right )^{2}} - \frac{\sqrt{- 2 x + 1}}{189 \left (3 x + 2\right )^{3}} - \frac{2245 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{64827} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(2+3*x)**4/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.102521, size = 58, normalized size = 0.66 \[ \frac{-\frac{21 \sqrt{1-2 x} \left (20205 x^2+25505 x+8056\right )}{(3 x+2)^3}-4490 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{129654} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]
[Out]
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Maple [A] time = 0.018, size = 57, normalized size = 0.7 \[ -108\,{\frac{1}{ \left ( -4-6\,x \right ) ^{3}} \left ( -{\frac{2245\, \left ( 1-2\,x \right ) ^{5/2}}{37044}}+{\frac{3265\, \left ( 1-2\,x \right ) ^{3/2}}{11907}}-{\frac{2111\,\sqrt{1-2\,x}}{6804}} \right ) }-{\frac{2245\,\sqrt{21}}{64827}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(2+3*x)^4/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.51419, size = 124, normalized size = 1.41 \[ \frac{2245}{129654} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) - \frac{20205 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 91420 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 103439 \, \sqrt{-2 \, x + 1}}{3087 \,{\left (27 \,{\left (2 \, x - 1\right )}^{3} + 189 \,{\left (2 \, x - 1\right )}^{2} + 882 \, x - 98\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21004, size = 120, normalized size = 1.36 \[ -\frac{\sqrt{21}{\left (\sqrt{21}{\left (20205 \, x^{2} + 25505 \, x + 8056\right )} \sqrt{-2 \, x + 1} - 2245 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{129654 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*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)**2/(2+3*x)**4/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.227387, size = 113, normalized size = 1.28 \[ \frac{2245}{129654} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{20205 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 91420 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 103439 \, \sqrt{-2 \, x + 1}}{24696 \,{\left (3 \, x + 2\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]