Optimal. Leaf size=129 \[ \frac{2}{25} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{31}{225} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{31 \sqrt{\frac{11}{3}} F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{1125}-\frac{1159 \sqrt{\frac{11}{3}} E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{1125} \]
[Out]
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Rubi [A] time = 0.259615, antiderivative size = 129, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.179 \[ \frac{2}{25} \sqrt{1-2 x} \sqrt{3 x+2} (5 x+3)^{3/2}-\frac{31}{225} \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-\frac{31 \sqrt{\frac{11}{3}} F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{1125}-\frac{1159 \sqrt{\frac{11}{3}} E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{1125} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x],x]
[Out]
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Rubi in Sympy [A] time = 24.0735, size = 114, normalized size = 0.88 \[ \frac{2 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{\frac{3}{2}} \sqrt{5 x + 3}}{15} - \frac{37 \sqrt{- 2 x + 1} \sqrt{3 x + 2} \sqrt{5 x + 3}}{225} - \frac{1159 \sqrt{33} E\left (\operatorname{asin}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}\middle | \frac{35}{33}\right )}{3375} - \frac{341 \sqrt{35} F\left (\operatorname{asin}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}\middle | \frac{33}{35}\right )}{39375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(1/2)*(2+3*x)**(1/2)*(3+5*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.245484, size = 97, normalized size = 0.75 \[ \frac{30 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3} (90 x+23)-1295 \sqrt{2} F\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )+2318 \sqrt{2} E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )}{6750} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x],x]
[Out]
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Maple [C] time = 0.013, size = 169, normalized size = 1.3 \[{\frac{1}{202500\,{x}^{3}+155250\,{x}^{2}-47250\,x-40500}\sqrt{1-2\,x}\sqrt{2+3\,x}\sqrt{3+5\,x} \left ( 1295\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) -2318\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) +81000\,{x}^{4}+82800\,{x}^{3}-3030\,{x}^{2}-21030\,x-4140 \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(1/2)*(2+3*x)^(1/2)*(3+5*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{- 2 x + 1} \sqrt{3 x + 2} \sqrt{5 x + 3}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(1/2)*(2+3*x)**(1/2)*(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1),x, algorithm="giac")
[Out]