Optimal. Leaf size=180 \[ \frac{4031135 \sqrt{1-2 x}}{1078 (5 x+3)}-\frac{182335 \sqrt{1-2 x}}{294 (5 x+3)^2}+\frac{4042 \sqrt{1-2 x}}{49 (3 x+2) (5 x+3)^2}+\frac{29 \sqrt{1-2 x}}{7 (3 x+2)^2 (5 x+3)^2}+\frac{\sqrt{1-2 x}}{3 (3 x+2)^3 (5 x+3)^2}+\frac{2528082}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )-\frac{551075}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
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Rubi [A] time = 0.369008, antiderivative size = 180, normalized size of antiderivative = 1., number of steps used = 10, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ \frac{4031135 \sqrt{1-2 x}}{1078 (5 x+3)}-\frac{182335 \sqrt{1-2 x}}{294 (5 x+3)^2}+\frac{4042 \sqrt{1-2 x}}{49 (3 x+2) (5 x+3)^2}+\frac{29 \sqrt{1-2 x}}{7 (3 x+2)^2 (5 x+3)^2}+\frac{\sqrt{1-2 x}}{3 (3 x+2)^3 (5 x+3)^2}+\frac{2528082}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )-\frac{551075}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 42.9798, size = 160, normalized size = 0.89 \[ \frac{2418681 \sqrt{- 2 x + 1}}{1078 \left (3 x + 2\right )} + \frac{28935 \sqrt{- 2 x + 1}}{77 \left (3 x + 2\right ) \left (5 x + 3\right )} - \frac{1745 \sqrt{- 2 x + 1}}{42 \left (3 x + 2\right ) \left (5 x + 3\right )^{2}} + \frac{29 \sqrt{- 2 x + 1}}{7 \left (3 x + 2\right )^{2} \left (5 x + 3\right )^{2}} + \frac{\sqrt{- 2 x + 1}}{3 \left (3 x + 2\right )^{3} \left (5 x + 3\right )^{2}} + \frac{2528082 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{343} - \frac{551075 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{121} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(1/2)/(2+3*x)**4/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.173552, size = 106, normalized size = 0.59 \[ \frac{\sqrt{1-2 x} \left (544203225 x^4+1396877220 x^3+1343346156 x^2+573620246 x+91763734\right )}{1078 (3 x+2)^3 (5 x+3)^2}+\frac{2528082}{49} \sqrt{\frac{3}{7}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )-\frac{551075}{11} \sqrt{\frac{5}{11}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^4*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.022, size = 103, normalized size = 0.6 \[ -972\,{\frac{1}{ \left ( -4-6\,x \right ) ^{3}} \left ({\frac{7297\, \left ( 1-2\,x \right ) ^{5/2}}{294}}-{\frac{22048\, \left ( 1-2\,x \right ) ^{3/2}}{189}}+{\frac{7403\,\sqrt{1-2\,x}}{54}} \right ) }+{\frac{2528082\,\sqrt{21}}{343}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) }+62500\,{\frac{1}{ \left ( -6-10\,x \right ) ^{2}} \left ( -{\frac{53\, \left ( 1-2\,x \right ) ^{3/2}}{220}}+{\frac{263\,\sqrt{1-2\,x}}{500}} \right ) }-{\frac{551075\,\sqrt{55}}{121}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(1/2)/(2+3*x)^4/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.53046, size = 221, normalized size = 1.23 \[ \frac{551075}{242} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{1264041}{343} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{544203225 \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - 4970567340 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + 17019867294 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 25893807436 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 14768524001 \, \sqrt{-2 \, x + 1}}{539 \,{\left (675 \,{\left (2 \, x - 1\right )}^{5} + 7695 \,{\left (2 \, x - 1\right )}^{4} + 35082 \,{\left (2 \, x - 1\right )}^{3} + 79954 \,{\left (2 \, x - 1\right )}^{2} + 182182 \, x - 49588\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/((5*x + 3)^3*(3*x + 2)^4),x, algorithm="maxima")
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Fricas [A] time = 0.222448, size = 267, normalized size = 1.48 \[ \frac{\sqrt{11} \sqrt{7}{\left (27002675 \, \sqrt{7} \sqrt{5}{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (\frac{\sqrt{11}{\left (5 \, x - 8\right )} + 11 \, \sqrt{5} \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) + 27808902 \, \sqrt{11} \sqrt{3}{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (\frac{\sqrt{7}{\left (3 \, x - 5\right )} - 7 \, \sqrt{3} \sqrt{-2 \, x + 1}}{3 \, x + 2}\right ) + \sqrt{11} \sqrt{7}{\left (544203225 \, x^{4} + 1396877220 \, x^{3} + 1343346156 \, x^{2} + 573620246 \, x + 91763734\right )} \sqrt{-2 \, x + 1}\right )}}{83006 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/((5*x + 3)^3*(3*x + 2)^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 141.276, size = 804, normalized size = 4.47 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(1/2)/(2+3*x)**4/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.247513, size = 204, normalized size = 1.13 \[ \frac{551075}{242} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{1264041}{343} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{125 \,{\left (1325 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 2893 \, \sqrt{-2 \, x + 1}\right )}}{44 \,{\left (5 \, x + 3\right )}^{2}} + \frac{9 \,{\left (65673 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 308672 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 362747 \, \sqrt{-2 \, x + 1}\right )}}{196 \,{\left (3 \, x + 2\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/((5*x + 3)^3*(3*x + 2)^4),x, algorithm="giac")
[Out]