Optimal. Leaf size=24 \[ -\frac{a^2}{4 x^4}-\frac{a b}{x^2}+b^2 \log (x) \]
[Out]
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Rubi [A] time = 0.0409143, antiderivative size = 24, 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 \[ -\frac{a^2}{4 x^4}-\frac{a b}{x^2}+b^2 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^2/x^5,x]
[Out]
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Rubi in Sympy [A] time = 7.16817, size = 24, normalized size = 1. \[ - \frac{a^{2}}{4 x^{4}} - \frac{a b}{x^{2}} + \frac{b^{2} \log{\left (x^{2} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**2/x**5,x)
[Out]
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Mathematica [A] time = 0.00150968, size = 24, normalized size = 1. \[ -\frac{a^2}{4 x^4}-\frac{a b}{x^2}+b^2 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^2/x^5,x]
[Out]
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Maple [A] time = 0.007, size = 23, normalized size = 1. \[ -{\frac{{a}^{2}}{4\,{x}^{4}}}-{\frac{ab}{{x}^{2}}}+{b}^{2}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^2/x^5,x)
[Out]
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Maxima [A] time = 1.34151, size = 35, normalized size = 1.46 \[ \frac{1}{2} \, b^{2} \log \left (x^{2}\right ) - \frac{4 \, a b x^{2} + a^{2}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202645, size = 38, normalized size = 1.58 \[ \frac{4 \, b^{2} x^{4} \log \left (x\right ) - 4 \, a b x^{2} - a^{2}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.27951, size = 22, normalized size = 0.92 \[ b^{2} \log{\left (x \right )} - \frac{a^{2} + 4 a b x^{2}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**2/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.210985, size = 46, normalized size = 1.92 \[ \frac{1}{2} \, b^{2}{\rm ln}\left (x^{2}\right ) - \frac{3 \, b^{2} x^{4} + 4 \, a b x^{2} + a^{2}}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2/x^5,x, algorithm="giac")
[Out]