Optimal. Leaf size=29 \[ -\frac{2 a}{5 x^{5/2}}-\frac{2 b}{\sqrt{x}}+\frac{2}{3} c x^{3/2} \]
[Out]
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Rubi [A] time = 0.0154632, 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 \[ -\frac{2 a}{5 x^{5/2}}-\frac{2 b}{\sqrt{x}}+\frac{2}{3} c x^{3/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 4.44683, size = 27, normalized size = 0.93 \[ - \frac{2 a}{5 x^{\frac{5}{2}}} - \frac{2 b}{\sqrt{x}} + \frac{2 c x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0118586, size = 25, normalized size = 0.86 \[ \frac{2 \left (-3 a-15 b x^2+5 c x^4\right )}{15 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)/x^(7/2),x]
[Out]
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Maple [A] time = 0.005, size = 22, normalized size = 0.8 \[ -{\frac{-10\,c{x}^{4}+30\,b{x}^{2}+6\,a}{15}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)/x^(7/2),x)
[Out]
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Maxima [A] time = 0.74058, size = 27, normalized size = 0.93 \[ \frac{2}{3} \, c x^{\frac{3}{2}} - \frac{2 \,{\left (5 \, b x^{2} + a\right )}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270259, size = 28, normalized size = 0.97 \[ \frac{2 \,{\left (5 \, c x^{4} - 15 \, b x^{2} - 3 \, a\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.8852, size = 27, normalized size = 0.93 \[ - \frac{2 a}{5 x^{\frac{5}{2}}} - \frac{2 b}{\sqrt{x}} + \frac{2 c x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.262108, size = 27, normalized size = 0.93 \[ \frac{2}{3} \, c x^{\frac{3}{2}} - \frac{2 \,{\left (5 \, b x^{2} + a\right )}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)/x^(7/2),x, algorithm="giac")
[Out]