Optimal. Leaf size=26 \[ \frac{(5 x+3) \log (5 x+3)}{10 \sqrt{(5 x+3)^2}} \]
[Out]
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Rubi [A] time = 0.0165697, antiderivative size = 26, 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 \[ \frac{(5 x+3) \log (10 x+6)}{10 \sqrt{(5 x+3)^2}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[(6 + 10*x)^2],x]
[Out]
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Rubi in Sympy [A] time = 1.77435, size = 26, normalized size = 1. \[ \frac{\left (100 x + 60\right ) \log{\left (5 x + 3 \right )}}{100 \sqrt{100 x^{2} + 120 x + 36}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/((6+10*x)**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0121235, size = 26, normalized size = 1. \[ \frac{(10 x+6) \log (10 x+6)}{10 \sqrt{(10 x+6)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[(6 + 10*x)^2],x]
[Out]
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Maple [A] time = 0.005, size = 26, normalized size = 1. \[{\frac{ \left ( 3+5\,x \right ) \sqrt{4}\ln \left ( 3+5\,x \right ) }{20}{\frac{1}{\sqrt{ \left ( 3+5\,x \right ) ^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/((6+10*x)^2)^(1/2),x)
[Out]
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Maxima [A] time = 1.47944, size = 8, normalized size = 0.31 \[ \frac{1}{10} \, \log \left (x + \frac{3}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/sqrt((5*x + 3)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211059, size = 11, normalized size = 0.42 \[ \frac{1}{10} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/sqrt((5*x + 3)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.101199, size = 7, normalized size = 0.27 \[ \frac{\log{\left (10 x + 6 \right )}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((6+10*x)**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215447, size = 20, normalized size = 0.77 \[ \frac{1}{10} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ){\rm sign}\left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/2/sqrt((5*x + 3)^2),x, algorithm="giac")
[Out]