Optimal. Leaf size=19 \[ 2 a \sqrt{x}+\frac{2}{5} b x^{5/2} \]
[Out]
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Rubi [A] time = 0.0140092, 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 \[ 2 a \sqrt{x}+\frac{2}{5} b x^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 2.93951, size = 17, normalized size = 0.89 \[ 2 a \sqrt{x} + \frac{2 b x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00774583, size = 19, normalized size = 1. \[ 2 a \sqrt{x}+\frac{2}{5} b x^{5/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)/Sqrt[x],x]
[Out]
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Maple [A] time = 0.005, size = 15, normalized size = 0.8 \[{\frac{2\,b{x}^{2}+10\,a}{5}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.3384, size = 18, normalized size = 0.95 \[ \frac{2}{5} \, b x^{\frac{5}{2}} + 2 \, a \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2191, size = 19, normalized size = 1. \[ \frac{2}{5} \,{\left (b x^{2} + 5 \, a\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.59789, size = 17, normalized size = 0.89 \[ 2 a \sqrt{x} + \frac{2 b x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.207556, size = 18, normalized size = 0.95 \[ \frac{2}{5} \, b x^{\frac{5}{2}} + 2 \, a \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)/sqrt(x),x, algorithm="giac")
[Out]