Optimal. Leaf size=21 \[ \frac{2}{3} a x^{3/2}+\frac{2}{11} c x^{11/2} \]
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Rubi [A] time = 0.0162625, antiderivative size = 21, 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 \[ \frac{2}{3} a x^{3/2}+\frac{2}{11} c x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(a + c*x^4),x]
[Out]
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Rubi in Sympy [A] time = 2.65604, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 c x^{\frac{11}{2}}}{11} \]
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 = 0.0071129, size = 21, normalized size = 1. \[ \frac{2}{3} a x^{3/2}+\frac{2}{11} c x^{11/2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(a + c*x^4),x]
[Out]
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Maple [A] time = 0.005, size = 16, normalized size = 0.8 \[{\frac{6\,c{x}^{4}+22\,a}{33}{x}^{{\frac{3}{2}}}} \]
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 = 1.50853, size = 18, normalized size = 0.86 \[ \frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}} \]
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 = 0.224774, size = 22, normalized size = 1.05 \[ \frac{2}{33} \,{\left (3 \, c x^{5} + 11 \, a x\right )} \sqrt{x} \]
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 = 2.30966, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 c x^{\frac{11}{2}}}{11} \]
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 = 0.213894, size = 18, normalized size = 0.86 \[ \frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)*sqrt(x),x, algorithm="giac")
[Out]