Optimal. Leaf size=29 \[ 2 a \sqrt{x}+\frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2} \]
[Out]
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Rubi [A] time = 0.0148693, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ 2 a \sqrt{x}+\frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 4.43351, size = 27, normalized size = 0.93 \[ 2 a \sqrt{x} + \frac{2 b x^{\frac{5}{2}}}{5} + \frac{2 c x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00889873, size = 25, normalized size = 0.86 \[ \frac{2}{45} \sqrt{x} \left (45 a+9 b x^2+5 c x^4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)/Sqrt[x],x]
[Out]
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Maple [A] time = 0.004, size = 22, normalized size = 0.8 \[{\frac{10\,c{x}^{4}+18\,b{x}^{2}+90\,a}{45}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)/x^(1/2),x)
[Out]
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Maxima [A] time = 0.748569, size = 26, normalized size = 0.9 \[ \frac{2}{9} \, c x^{\frac{9}{2}} + \frac{2}{5} \, b x^{\frac{5}{2}} + 2 \, a \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270266, size = 28, normalized size = 0.97 \[ \frac{2}{45} \,{\left (5 \, c x^{4} + 9 \, b x^{2} + 45 \, a\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.96356, size = 27, normalized size = 0.93 \[ 2 a \sqrt{x} + \frac{2 b x^{\frac{5}{2}}}{5} + \frac{2 c x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.25977, size = 26, normalized size = 0.9 \[ \frac{2}{9} \, c x^{\frac{9}{2}} + \frac{2}{5} \, b x^{\frac{5}{2}} + 2 \, a \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)/sqrt(x),x, algorithm="giac")
[Out]