Optimal. Leaf size=42 \[ \frac{1}{12} \left (4 x^2+12 x+9\right )^{3/2}-\frac{3}{8} (2 x+3) \sqrt{4 x^2+12 x+9} \]
[Out]
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Rubi [A] time = 0.031837, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{1}{12} \left (4 x^2+12 x+9\right )^{3/2}-\frac{3}{8} (2 x+3) \sqrt{4 x^2+12 x+9} \]
Antiderivative was successfully verified.
[In] Int[x*Sqrt[9 + 12*x + 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 3.70171, size = 36, normalized size = 0.86 \[ - \frac{3 \left (8 x + 12\right ) \sqrt{4 x^{2} + 12 x + 9}}{32} + \frac{\left (4 x^{2} + 12 x + 9\right )^{\frac{3}{2}}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(4*x**2+12*x+9)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0125517, size = 30, normalized size = 0.71 \[ \frac{x^2 \sqrt{(2 x+3)^2} (4 x+9)}{6 (2 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[x*Sqrt[9 + 12*x + 4*x^2],x]
[Out]
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Maple [A] time = 0.004, size = 27, normalized size = 0.6 \[{\frac{{x}^{2} \left ( 4\,x+9 \right ) }{12\,x+18}\sqrt{ \left ( 2\,x+3 \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(4*x^2+12*x+9)^(1/2),x)
[Out]
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Maxima [A] time = 0.825536, size = 59, normalized size = 1.4 \[ \frac{1}{12} \,{\left (4 \, x^{2} + 12 \, x + 9\right )}^{\frac{3}{2}} - \frac{3}{4} \, \sqrt{4 \, x^{2} + 12 \, x + 9} x - \frac{9}{8} \, \sqrt{4 \, x^{2} + 12 \, x + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 12*x + 9)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217213, size = 15, normalized size = 0.36 \[ \frac{2}{3} \, x^{3} + \frac{3}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 12*x + 9)*x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x \sqrt{\left (2 x + 3\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(4*x**2+12*x+9)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.207888, size = 42, normalized size = 1. \[ \frac{2}{3} \, x^{3}{\rm sign}\left (2 \, x + 3\right ) + \frac{3}{2} \, x^{2}{\rm sign}\left (2 \, x + 3\right ) - \frac{9}{8} \,{\rm sign}\left (2 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 12*x + 9)*x,x, algorithm="giac")
[Out]