Optimal. Leaf size=23 \[ -\frac{a^2}{3 x^3}-\frac{2 a b}{x}+b^2 x \]
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Rubi [A] time = 0.0304979, antiderivative size = 23, 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 \[ -\frac{a^2}{3 x^3}-\frac{2 a b}{x}+b^2 x \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^2/x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{2}}{3 x^{3}} - \frac{2 a b}{x} + \int b^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**2/x**4,x)
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Mathematica [A] time = 0.00149176, size = 23, normalized size = 1. \[ -\frac{a^2}{3 x^3}-\frac{2 a b}{x}+b^2 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^2/x^4,x]
[Out]
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Maple [A] time = 0.007, size = 22, normalized size = 1. \[ -{\frac{{a}^{2}}{3\,{x}^{3}}}-2\,{\frac{ab}{x}}+{b}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^2/x^4,x)
[Out]
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Maxima [A] time = 1.33237, size = 30, normalized size = 1.3 \[ b^{2} x - \frac{6 \, a b x^{2} + a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2/x^4,x, algorithm="maxima")
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Fricas [A] time = 0.193146, size = 35, normalized size = 1.52 \[ \frac{3 \, b^{2} x^{4} - 6 \, a b x^{2} - a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.13156, size = 20, normalized size = 0.87 \[ b^{2} x - \frac{a^{2} + 6 a b x^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**2/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.207674, size = 30, normalized size = 1.3 \[ b^{2} x - \frac{6 \, a b x^{2} + a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^2/x^4,x, algorithm="giac")
[Out]