Optimal. Leaf size=14 \[ \frac{\log \left (\sqrt{a}+x\right )}{\sqrt{a}} \]
[Out]
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Rubi [A] time = 0.00783638, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{\log \left (\sqrt{a}+x\right )}{\sqrt{a}} \]
Antiderivative was successfully verified.
[In] Int[(a + Sqrt[a]*x)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.25852, size = 12, normalized size = 0.86 \[ \frac{\log{\left (\sqrt{a} + x \right )}}{\sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+x*a**(1/2)),x)
[Out]
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Mathematica [A] time = 0.00512005, size = 16, normalized size = 1.14 \[ \frac{\log \left (\sqrt{a} x+a\right )}{\sqrt{a}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + Sqrt[a]*x)^(-1),x]
[Out]
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Maple [A] time = 0., size = 13, normalized size = 0.9 \[{1\ln \left ( a+x\sqrt{a} \right ){\frac{1}{\sqrt{a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+x*a^(1/2)),x)
[Out]
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Maxima [A] time = 1.35896, size = 16, normalized size = 1.14 \[ \frac{\log \left (\sqrt{a} x + a\right )}{\sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a)*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218018, size = 16, normalized size = 1.14 \[ \frac{\log \left (\sqrt{a} x + a\right )}{\sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a)*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.084568, size = 14, normalized size = 1. \[ \frac{\log{\left (\sqrt{a} x + a \right )}}{\sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+x*a**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.204295, size = 18, normalized size = 1.29 \[ \frac{{\rm ln}\left ({\left | \sqrt{a} x + a \right |}\right )}{\sqrt{a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a)*x + a),x, algorithm="giac")
[Out]