Optimal. Leaf size=201 \[ \frac{7 (1-2 x)^{3/2}}{12 (3 x+2)^4 (5 x+3)^2}+\frac{23680975 \sqrt{1-2 x}}{168 (5 x+3)}+\frac{522385 \sqrt{1-2 x}}{168 (3 x+2) (5 x+3)^2}+\frac{11243 \sqrt{1-2 x}}{72 (3 x+2)^2 (5 x+3)^2}+\frac{1393 \sqrt{1-2 x}}{108 (3 x+2)^3 (5 x+3)^2}-\frac{8836825 \sqrt{1-2 x}}{378 (5 x+3)^2}+\frac{163363895 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{28 \sqrt{21}}-171675 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
[Out]
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Rubi [A] time = 0.45996, antiderivative size = 201, normalized size of antiderivative = 1., number of steps used = 11, number of rules used = 6, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{7 (1-2 x)^{3/2}}{12 (3 x+2)^4 (5 x+3)^2}+\frac{23680975 \sqrt{1-2 x}}{168 (5 x+3)}+\frac{522385 \sqrt{1-2 x}}{168 (3 x+2) (5 x+3)^2}+\frac{11243 \sqrt{1-2 x}}{72 (3 x+2)^2 (5 x+3)^2}+\frac{1393 \sqrt{1-2 x}}{108 (3 x+2)^3 (5 x+3)^2}-\frac{8836825 \sqrt{1-2 x}}{378 (5 x+3)^2}+\frac{163363895 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{28 \sqrt{21}}-171675 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 48.5419, size = 182, normalized size = 0.91 \[ \frac{7 \left (- 2 x + 1\right )^{\frac{3}{2}}}{12 \left (3 x + 2\right )^{4} \left (5 x + 3\right )^{2}} + \frac{23680975 \sqrt{- 2 x + 1}}{168 \left (5 x + 3\right )} - \frac{8836825 \sqrt{- 2 x + 1}}{378 \left (5 x + 3\right )^{2}} + \frac{522385 \sqrt{- 2 x + 1}}{168 \left (3 x + 2\right ) \left (5 x + 3\right )^{2}} + \frac{11243 \sqrt{- 2 x + 1}}{72 \left (3 x + 2\right )^{2} \left (5 x + 3\right )^{2}} + \frac{1393 \sqrt{- 2 x + 1}}{108 \left (3 x + 2\right )^{3} \left (5 x + 3\right )^{2}} + \frac{163363895 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{588} - 171675 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(5/2)/(2+3*x)**5/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.215936, size = 105, normalized size = 0.52 \[ \frac{\sqrt{1-2 x} \left (3196931625 x^5+10337268075 x^4+13362164665 x^3+8630749831 x^2+2785562634 x+359378534\right )}{56 (3 x+2)^4 (5 x+3)^2}+\frac{163363895 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{28 \sqrt{21}}-171675 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^5*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.023, size = 112, normalized size = 0.6 \[ -162\,{\frac{1}{ \left ( -4-6\,x \right ) ^{4}} \left ({\frac{3170015\, \left ( 1-2\,x \right ) ^{7/2}}{168}}-{\frac{28695733\, \left ( 1-2\,x \right ) ^{5/2}}{216}}+{\frac{202051885\, \left ( 1-2\,x \right ) ^{3/2}}{648}}-{\frac{52696315\,\sqrt{1-2\,x}}{216}} \right ) }+{\frac{163363895\,\sqrt{21}}{588}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) }+13750\,{\frac{1}{ \left ( -6-10\,x \right ) ^{2}} \left ( -{\frac{339\, \left ( 1-2\,x \right ) ^{3/2}}{10}}+{\frac{3707\,\sqrt{1-2\,x}}{50}} \right ) }-171675\,{\it Artanh} \left ( 1/11\,\sqrt{55}\sqrt{1-2\,x} \right ) \sqrt{55} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(5/2)/(2+3*x)^5/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.52273, size = 246, normalized size = 1.22 \[ \frac{171675}{2} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{163363895}{1176} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) - \frac{3196931625 \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - 36659194275 \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + 168116119510 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 385408507778 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 441689778145 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 202435240315 \, \sqrt{-2 \, x + 1}}{28 \,{\left (2025 \,{\left (2 \, x - 1\right )}^{6} + 27810 \,{\left (2 \, x - 1\right )}^{5} + 159111 \,{\left (2 \, x - 1\right )}^{4} + 485436 \,{\left (2 \, x - 1\right )}^{3} + 832951 \,{\left (2 \, x - 1\right )}^{2} + 1524292 \, x - 471625\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(5/2)/((5*x + 3)^3*(3*x + 2)^5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.243986, size = 266, normalized size = 1.32 \[ \frac{\sqrt{21}{\left (4806900 \, \sqrt{55} \sqrt{21}{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (\frac{5 \, x + \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right ) + \sqrt{21}{\left (3196931625 \, x^{5} + 10337268075 \, x^{4} + 13362164665 \, x^{3} + 8630749831 \, x^{2} + 2785562634 \, x + 359378534\right )} \sqrt{-2 \, x + 1} + 163363895 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} - 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{1176 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(5/2)/((5*x + 3)^3*(3*x + 2)^5),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)/(2+3*x)**5/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.220327, size = 225, normalized size = 1.12 \[ \frac{171675}{2} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{163363895}{1176} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{275 \,{\left (1695 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 3707 \, \sqrt{-2 \, x + 1}\right )}}{4 \,{\left (5 \, x + 3\right )}^{2}} + \frac{85590405 \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + 602610393 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 1414363195 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 1106622615 \, \sqrt{-2 \, x + 1}}{448 \,{\left (3 \, x + 2\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(5/2)/((5*x + 3)^3*(3*x + 2)^5),x, algorithm="giac")
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