Optimal. Leaf size=31 \[ \frac{b^2 \log (a x+b)}{a^3}-\frac{b x}{a^2}+\frac{x^2}{2 a} \]
[Out]
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Rubi [A] time = 0.0483696, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{b^2 \log (a x+b)}{a^3}-\frac{b x}{a^2}+\frac{x^2}{2 a} \]
Antiderivative was successfully verified.
[In] Int[x/(a + b/x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\int x\, dx}{a} - \frac{\int b\, dx}{a^{2}} + \frac{b^{2} \log{\left (a x + b \right )}}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(a+b/x),x)
[Out]
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Mathematica [A] time = 0.00557378, size = 31, normalized size = 1. \[ \frac{b^2 \log (a x+b)}{a^3}-\frac{b x}{a^2}+\frac{x^2}{2 a} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a + b/x),x]
[Out]
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Maple [A] time = 0.003, size = 30, normalized size = 1. \[ -{\frac{bx}{{a}^{2}}}+{\frac{{x}^{2}}{2\,a}}+{\frac{{b}^{2}\ln \left ( ax+b \right ) }{{a}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(a+b/x),x)
[Out]
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Maxima [A] time = 1.43764, size = 39, normalized size = 1.26 \[ \frac{b^{2} \log \left (a x + b\right )}{a^{3}} + \frac{a x^{2} - 2 \, b x}{2 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a + b/x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217784, size = 39, normalized size = 1.26 \[ \frac{a^{2} x^{2} - 2 \, a b x + 2 \, b^{2} \log \left (a x + b\right )}{2 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a + b/x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.09741, size = 26, normalized size = 0.84 \[ \frac{x^{2}}{2 a} - \frac{b x}{a^{2}} + \frac{b^{2} \log{\left (a x + b \right )}}{a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a+b/x),x)
[Out]
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GIAC/XCAS [A] time = 0.223661, size = 41, normalized size = 1.32 \[ \frac{b^{2}{\rm ln}\left ({\left | a x + b \right |}\right )}{a^{3}} + \frac{a x^{2} - 2 \, b x}{2 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(a + b/x),x, algorithm="giac")
[Out]