Optimal. Leaf size=19 \[ 2 a \sqrt{x}+\frac{2}{9} c x^{9/2} \]
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Rubi [A] time = 0.0137599, 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 \[ 2 a \sqrt{x}+\frac{2}{9} c x^{9/2} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 2.63539, size = 17, normalized size = 0.89 \[ 2 a \sqrt{x} + \frac{2 c x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00657469, size = 19, normalized size = 1. \[ 2 a \sqrt{x}+\frac{2}{9} c x^{9/2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)/Sqrt[x],x]
[Out]
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Maple [A] time = 0.003, size = 15, normalized size = 0.8 \[{\frac{2\,c{x}^{4}+18\,a}{9}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)/x^(1/2),x)
[Out]
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Maxima [A] time = 1.43583, size = 18, normalized size = 0.95 \[ \frac{2}{9} \, c x^{\frac{9}{2}} + 2 \, a \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.239344, size = 19, normalized size = 1. \[ \frac{2}{9} \,{\left (c x^{4} + 9 \, a\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.95418, size = 17, normalized size = 0.89 \[ 2 a \sqrt{x} + \frac{2 c x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211987, size = 18, normalized size = 0.95 \[ \frac{2}{9} \, c x^{\frac{9}{2}} + 2 \, a \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)/sqrt(x),x, algorithm="giac")
[Out]