Optimal. Leaf size=19 \[ \frac{2}{3} a x^{3/2}+2 b \sqrt{x} \]
[Out]
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Rubi [A] time = 0.0136521, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{2}{3} a x^{3/2}+2 b \sqrt{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)*Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 2.85467, size = 17, normalized size = 0.89 \[ \frac{2 a x^{\frac{3}{2}}}{3} + 2 b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)*x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00542563, size = 16, normalized size = 0.84 \[ \frac{2}{3} \sqrt{x} (a x+3 b) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)*Sqrt[x],x]
[Out]
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Maple [A] time = 0.005, size = 13, normalized size = 0.7 \[{\frac{2\,ax+6\,b}{3}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)*x^(1/2),x)
[Out]
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Maxima [A] time = 1.43671, size = 18, normalized size = 0.95 \[ \frac{2}{3} \,{\left (a + \frac{3 \, b}{x}\right )} x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)*sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224643, size = 16, normalized size = 0.84 \[ \frac{2}{3} \,{\left (a x + 3 \, b\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)*sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.545696, size = 17, normalized size = 0.89 \[ \frac{2 a x^{\frac{3}{2}}}{3} + 2 b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)*x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.222567, size = 18, normalized size = 0.95 \[ \frac{2}{3} \, a x^{\frac{3}{2}} + 2 \, b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)*sqrt(x),x, algorithm="giac")
[Out]