Optimal. Leaf size=34 \[ 2 a^2 \sqrt{x}+\frac{4}{9} a c x^{9/2}+\frac{2}{17} c^2 x^{17/2} \]
[Out]
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Rubi [A] time = 0.0262335, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ 2 a^2 \sqrt{x}+\frac{4}{9} a c x^{9/2}+\frac{2}{17} c^2 x^{17/2} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)^2/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 4.572, size = 32, normalized size = 0.94 \[ 2 a^{2} \sqrt{x} + \frac{4 a c x^{\frac{9}{2}}}{9} + \frac{2 c^{2} x^{\frac{17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**2/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0115658, size = 30, normalized size = 0.88 \[ \frac{2}{153} \sqrt{x} \left (153 a^2+34 a c x^4+9 c^2 x^8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)^2/Sqrt[x],x]
[Out]
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \[{\frac{18\,{c}^{2}{x}^{8}+68\,ac{x}^{4}+306\,{a}^{2}}{153}\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^2/x^(1/2),x)
[Out]
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Maxima [A] time = 1.43623, size = 32, normalized size = 0.94 \[ \frac{2}{17} \, c^{2} x^{\frac{17}{2}} + \frac{4}{9} \, a c x^{\frac{9}{2}} + 2 \, a^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22316, size = 35, normalized size = 1.03 \[ \frac{2}{153} \,{\left (9 \, c^{2} x^{8} + 34 \, a c x^{4} + 153 \, a^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 15.4393, size = 32, normalized size = 0.94 \[ 2 a^{2} \sqrt{x} + \frac{4 a c x^{\frac{9}{2}}}{9} + \frac{2 c^{2} x^{\frac{17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**2/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.2112, size = 32, normalized size = 0.94 \[ \frac{2}{17} \, c^{2} x^{\frac{17}{2}} + \frac{4}{9} \, a c x^{\frac{9}{2}} + 2 \, a^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^2/sqrt(x),x, algorithm="giac")
[Out]