Optimal. Leaf size=43 \[ -\frac{1}{12} \sqrt{-3 x^2+5 x+2} (5-6 x)-\frac{49 \sin ^{-1}\left (\frac{1}{7} (5-6 x)\right )}{24 \sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0288746, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ -\frac{1}{12} \sqrt{-3 x^2+5 x+2} (5-6 x)-\frac{49 \sin ^{-1}\left (\frac{1}{7} (5-6 x)\right )}{24 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[2 + 5*x - 3*x^2],x]
[Out]
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Rubi in Sympy [A] time = 2.07932, size = 56, normalized size = 1.3 \[ - \frac{\left (- 6 x + 5\right ) \sqrt{- 3 x^{2} + 5 x + 2}}{12} - \frac{49 \sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \left (- 6 x + 5\right )}{6 \sqrt{- 3 x^{2} + 5 x + 2}} \right )}}{72} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-3*x**2+5*x+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0336152, size = 44, normalized size = 1.02 \[ \left (\frac{x}{2}-\frac{5}{12}\right ) \sqrt{-3 x^2+5 x+2}-\frac{49 \sin ^{-1}\left (\frac{1}{7} (5-6 x)\right )}{24 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[2 + 5*x - 3*x^2],x]
[Out]
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Maple [A] time = 0.004, size = 32, normalized size = 0.7 \[{\frac{49\,\sqrt{3}}{72}\arcsin \left ( -{\frac{5}{7}}+{\frac{6\,x}{7}} \right ) }-{\frac{5-6\,x}{12}\sqrt{-3\,{x}^{2}+5\,x+2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-3*x^2+5*x+2)^(1/2),x)
[Out]
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Maxima [A] time = 0.820811, size = 55, normalized size = 1.28 \[ \frac{1}{2} \, \sqrt{-3 \, x^{2} + 5 \, x + 2} x - \frac{49}{72} \, \sqrt{3} \arcsin \left (-\frac{6}{7} \, x + \frac{5}{7}\right ) - \frac{5}{12} \, \sqrt{-3 \, x^{2} + 5 \, x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*x^2 + 5*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224465, size = 72, normalized size = 1.67 \[ \frac{1}{72} \, \sqrt{3}{\left (2 \, \sqrt{3} \sqrt{-3 \, x^{2} + 5 \, x + 2}{\left (6 \, x - 5\right )} + 49 \, \arctan \left (\frac{\sqrt{3}{\left (6 \, x - 5\right )}}{6 \, \sqrt{-3 \, x^{2} + 5 \, x + 2}}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*x^2 + 5*x + 2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{- 3 x^{2} + 5 x + 2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3*x**2+5*x+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21008, size = 42, normalized size = 0.98 \[ \frac{1}{12} \, \sqrt{-3 \, x^{2} + 5 \, x + 2}{\left (6 \, x - 5\right )} + \frac{49}{72} \, \sqrt{3} \arcsin \left (\frac{6}{7} \, x - \frac{5}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-3*x^2 + 5*x + 2),x, algorithm="giac")
[Out]