Optimal. Leaf size=39 \[ -\frac{a^3}{6 x^6}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{2 x^2}+b^3 \log (x) \]
[Out]
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Rubi [A] time = 0.0528071, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^3}{6 x^6}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{2 x^2}+b^3 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^3/x^7,x]
[Out]
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Rubi in Sympy [A] time = 9.02265, size = 41, normalized size = 1.05 \[ - \frac{a^{3}}{6 x^{6}} - \frac{3 a^{2} b}{4 x^{4}} - \frac{3 a b^{2}}{2 x^{2}} + \frac{b^{3} \log{\left (x^{2} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**3/x**7,x)
[Out]
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Mathematica [A] time = 0.00772855, size = 39, normalized size = 1. \[ -\frac{a^3}{6 x^6}-\frac{3 a^2 b}{4 x^4}-\frac{3 a b^2}{2 x^2}+b^3 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^3/x^7,x]
[Out]
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Maple [A] time = 0.009, size = 34, normalized size = 0.9 \[ -{\frac{{a}^{3}}{6\,{x}^{6}}}-{\frac{3\,{a}^{2}b}{4\,{x}^{4}}}-{\frac{3\,a{b}^{2}}{2\,{x}^{2}}}+{b}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^3/x^7,x)
[Out]
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Maxima [A] time = 1.346, size = 53, normalized size = 1.36 \[ \frac{1}{2} \, b^{3} \log \left (x^{2}\right ) - \frac{18 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202058, size = 53, normalized size = 1.36 \[ \frac{12 \, b^{3} x^{6} \log \left (x\right ) - 18 \, a b^{2} x^{4} - 9 \, a^{2} b x^{2} - 2 \, a^{3}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.49431, size = 36, normalized size = 0.92 \[ b^{3} \log{\left (x \right )} - \frac{2 a^{3} + 9 a^{2} b x^{2} + 18 a b^{2} x^{4}}{12 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**3/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.207988, size = 63, normalized size = 1.62 \[ \frac{1}{2} \, b^{3}{\rm ln}\left (x^{2}\right ) - \frac{11 \, b^{3} x^{6} + 18 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} + 2 \, a^{3}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^3/x^7,x, algorithm="giac")
[Out]