Optimal. Leaf size=20 \[ \frac{1}{10} (5 x+3) \sqrt{(5 x+3)^2} \]
[Out]
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Rubi [A] time = 0.0143624, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ \frac{1}{10} (5 x+3) \sqrt{(5 x+3)^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[(3 + 5*x)^2],x]
[Out]
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Rubi in Sympy [A] time = 1.38744, size = 19, normalized size = 0.95 \[ \frac{\left (50 x + 30\right ) \sqrt{25 x^{2} + 30 x + 9}}{100} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(((3+5*x)**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0145698, size = 25, normalized size = 1.25 \[ \frac{x \sqrt{(5 x+3)^2} (5 x+6)}{10 x+6} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[(3 + 5*x)^2],x]
[Out]
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Maple [A] time = 0.004, size = 25, normalized size = 1.3 \[{\frac{x \left ( 5\,x+6 \right ) }{6+10\,x}\sqrt{ \left ( 3+5\,x \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(((3+5*x)^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.51976, size = 41, normalized size = 2.05 \[ \frac{1}{2} \, \sqrt{25 \, x^{2} + 30 \, x + 9} x + \frac{3}{10} \, \sqrt{25 \, x^{2} + 30 \, x + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((5*x + 3)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208223, size = 12, normalized size = 0.6 \[ \frac{5}{2} \, x^{2} + 3 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((5*x + 3)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.095481, size = 8, normalized size = 0.4 \[ \frac{5 x^{2}}{2} + 3 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((3+5*x)**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217768, size = 35, normalized size = 1.75 \[ \frac{1}{2} \,{\left (5 \, x^{2} + 6 \, x\right )}{\rm sign}\left (5 \, x + 3\right ) + \frac{9}{10} \,{\rm sign}\left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt((5*x + 3)^2),x, algorithm="giac")
[Out]