Optimal. Leaf size=22 \[ a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0125757, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[a + d/x^3 + c/x^2 + b/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ b \log{\left (x \right )} - \frac{c}{x} - \frac{d}{2 x^{2}} + \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(a+d/x**3+c/x**2+b/x,x)
[Out]
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Mathematica [A] time = 0.00997067, size = 22, normalized size = 1. \[ a x+b \log (x)-\frac{c}{x}-\frac{d}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[a + d/x^3 + c/x^2 + b/x,x]
[Out]
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Maple [A] time = 0.003, size = 21, normalized size = 1. \[ -{\frac{d}{2\,{x}^{2}}}-{\frac{c}{x}}+ax+b\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(a+d/x^3+c/x^2+b/x,x)
[Out]
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Maxima [A] time = 1.33844, size = 27, normalized size = 1.23 \[ a x + b \log \left (x\right ) - \frac{c}{x} - \frac{d}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a + b/x + c/x^2 + d/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198006, size = 36, normalized size = 1.64 \[ \frac{2 \, a x^{3} + 2 \, b x^{2} \log \left (x\right ) - 2 \, c x - d}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a + b/x + c/x^2 + d/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.62331, size = 19, normalized size = 0.86 \[ a x + b \log{\left (x \right )} - \frac{2 c x + d}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a+d/x**3+c/x**2+b/x,x)
[Out]
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GIAC/XCAS [A] time = 0.26164, size = 28, normalized size = 1.27 \[ a x + b{\rm ln}\left ({\left | x \right |}\right ) - \frac{c}{x} - \frac{d}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a + b/x + c/x^2 + d/x^3,x, algorithm="giac")
[Out]