Optimal. Leaf size=19 \[ \frac{2}{7} c x^{7/2}-\frac{2 a}{\sqrt{x}} \]
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Rubi [A] time = 0.0117597, 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 \[ \frac{2}{7} c x^{7/2}-\frac{2 a}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)/x^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.62062, size = 17, normalized size = 0.89 \[ - \frac{2 a}{\sqrt{x}} + \frac{2 c x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)/x**(3/2),x)
[Out]
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Mathematica [A] time = 0.00802901, size = 19, normalized size = 1. \[ \frac{2}{7} c x^{7/2}-\frac{2 a}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)/x^(3/2),x]
[Out]
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Maple [A] time = 0.004, size = 16, normalized size = 0.8 \[ -{\frac{-2\,c{x}^{4}+14\,a}{7}{\frac{1}{\sqrt{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)/x^(3/2),x)
[Out]
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Maxima [A] time = 1.43631, size = 18, normalized size = 0.95 \[ \frac{2}{7} \, c x^{\frac{7}{2}} - \frac{2 \, a}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)/x^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236784, size = 19, normalized size = 1. \[ \frac{2 \,{\left (c x^{4} - 7 \, a\right )}}{7 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)/x^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.12702, size = 17, normalized size = 0.89 \[ - \frac{2 a}{\sqrt{x}} + \frac{2 c x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)/x**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212452, size = 18, normalized size = 0.95 \[ \frac{2}{7} \, c x^{\frac{7}{2}} - \frac{2 \, a}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)/x^(3/2),x, algorithm="giac")
[Out]