Optimal. Leaf size=40 \[ \frac{2 \sqrt{x}}{b}-\frac{2 \sqrt{a} \tan ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{b^{3/2}} \]
[Out]
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Rubi [A] time = 0.0319913, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{2 \sqrt{x}}{b}-\frac{2 \sqrt{a} \tan ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{b^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]/(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 6.25855, size = 36, normalized size = 0.9 \[ - \frac{2 \sqrt{a} \operatorname{atan}{\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right )}}{b^{\frac{3}{2}}} + \frac{2 \sqrt{x}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(1/2)/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.0164958, size = 40, normalized size = 1. \[ \frac{2 \sqrt{x}}{b}-\frac{2 \sqrt{a} \tan ^{-1}\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right )}{b^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]/(a + b*x),x]
[Out]
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Maple [A] time = 0.009, size = 32, normalized size = 0.8 \[ 2\,{\frac{\sqrt{x}}{b}}-2\,{\frac{a}{b\sqrt{ab}}\arctan \left ({\frac{b\sqrt{x}}{\sqrt{ab}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(1/2)/(b*x+a),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220579, size = 1, normalized size = 0.02 \[ \left [\frac{\sqrt{-\frac{a}{b}} \log \left (\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right ) + 2 \, \sqrt{x}}{b}, -\frac{2 \,{\left (\sqrt{\frac{a}{b}} \arctan \left (\frac{\sqrt{x}}{\sqrt{\frac{a}{b}}}\right ) - \sqrt{x}\right )}}{b}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.85297, size = 36, normalized size = 0.9 \[ - \frac{2 \sqrt{a} \operatorname{atan}{\left (\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}} \right )}}{b^{\frac{3}{2}}} + \frac{2 \sqrt{x}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(1/2)/(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.207195, size = 42, normalized size = 1.05 \[ -\frac{2 \, a \arctan \left (\frac{b \sqrt{x}}{\sqrt{a b}}\right )}{\sqrt{a b} b} + \frac{2 \, \sqrt{x}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)/(b*x + a),x, algorithm="giac")
[Out]