Optimal. Leaf size=20 \[ -\frac{a^2}{x}+2 a b \log (x)+b^2 x \]
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Rubi [A] time = 0.0220168, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^2}{x}+2 a b \log (x)+b^2 x \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^2/x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{2}}{x} + 2 a b \log{\left (x \right )} + \int b^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2/x**2,x)
[Out]
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Mathematica [A] time = 0.00155256, size = 20, normalized size = 1. \[ -\frac{a^2}{x}+2 a b \log (x)+b^2 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^2/x^2,x]
[Out]
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Maple [A] time = 0.007, size = 21, normalized size = 1.1 \[ -{\frac{{a}^{2}}{x}}+{b}^{2}x+2\,ab\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2/x^2,x)
[Out]
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Maxima [A] time = 1.33993, size = 27, normalized size = 1.35 \[ b^{2} x + 2 \, a b \log \left (x\right ) - \frac{a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19319, size = 32, normalized size = 1.6 \[ \frac{b^{2} x^{2} + 2 \, a b x \log \left (x\right ) - a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.06526, size = 17, normalized size = 0.85 \[ - \frac{a^{2}}{x} + 2 a b \log{\left (x \right )} + b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**2/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.210489, size = 28, normalized size = 1.4 \[ b^{2} x + 2 \, a b{\rm ln}\left ({\left | x \right |}\right ) - \frac{a^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/x^2,x, algorithm="giac")
[Out]