Optimal. Leaf size=21 \[ \frac{\log \left (1-(-a)^{3/2} x\right )}{\sqrt{-a}} \]
[Out]
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Rubi [A] time = 0.0125565, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\log \left (1-(-a)^{3/2} x\right )}{\sqrt{-a}} \]
Antiderivative was successfully verified.
[In] Int[(a^(-1) + Sqrt[-a]*x)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.86478, size = 17, normalized size = 0.81 \[ \frac{\log{\left (- x \left (- a\right )^{\frac{3}{2}} + 1 \right )}}{\sqrt{- a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1/a+x*(-a)**(1/2)),x)
[Out]
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Mathematica [A] time = 0.00974668, size = 21, normalized size = 1. \[ \frac{\log \left (\sqrt{-a} a x+1\right )}{\sqrt{-a}} \]
Antiderivative was successfully verified.
[In] Integrate[(a^(-1) + Sqrt[-a]*x)^(-1),x]
[Out]
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Maple [A] time = 0.001, size = 19, normalized size = 0.9 \[{1\ln \left ({a}^{-1}+x\sqrt{-a} \right ){\frac{1}{\sqrt{-a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1/a+x*(-a)^(1/2)),x)
[Out]
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Maxima [A] time = 1.34056, size = 24, normalized size = 1.14 \[ \frac{\log \left (\sqrt{-a} x + \frac{1}{a}\right )}{\sqrt{-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-a)*x + 1/a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217417, size = 23, normalized size = 1.1 \[ \frac{\log \left (\sqrt{-a} a x + 1\right )}{\sqrt{-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-a)*x + 1/a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.113746, size = 19, normalized size = 0.9 \[ \frac{\log{\left (a x \sqrt{- a} + 1 \right )}}{\sqrt{- a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1/a+x*(-a)**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.206434, size = 26, normalized size = 1.24 \[ \frac{{\rm ln}\left ({\left | \sqrt{-a} x + \frac{1}{a} \right |}\right )}{\sqrt{-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-a)*x + 1/a),x, algorithm="giac")
[Out]