Optimal. Leaf size=20 \[ \frac{21}{2 \left (x^2+5\right )}+2 \log \left (x^2+5\right ) \]
[Out]
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Rubi [A] time = 0.049741, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ \frac{21}{2 \left (x^2+5\right )}+2 \log \left (x^2+5\right ) \]
Antiderivative was successfully verified.
[In] Int[(-x + 4*x^3)/(5 + x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 9.17442, size = 15, normalized size = 0.75 \[ 2 \log{\left (x^{2} + 5 \right )} + \frac{21}{2 \left (x^{2} + 5\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((4*x**3-x)/(x**2+5)**2,x)
[Out]
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Mathematica [A] time = 0.0126905, size = 20, normalized size = 1. \[ \frac{21}{2 \left (x^2+5\right )}+2 \log \left (x^2+5\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(-x + 4*x^3)/(5 + x^2)^2,x]
[Out]
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Maple [A] time = 0.014, size = 19, normalized size = 1. \[{\frac{21}{2\,{x}^{2}+10}}+2\,\ln \left ({x}^{2}+5 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((4*x^3-x)/(x^2+5)^2,x)
[Out]
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Maxima [A] time = 1.34696, size = 24, normalized size = 1.2 \[ \frac{21}{2 \,{\left (x^{2} + 5\right )}} + 2 \, \log \left (x^{2} + 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^3 - x)/(x^2 + 5)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223175, size = 32, normalized size = 1.6 \[ \frac{4 \,{\left (x^{2} + 5\right )} \log \left (x^{2} + 5\right ) + 21}{2 \,{\left (x^{2} + 5\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^3 - x)/(x^2 + 5)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.097345, size = 15, normalized size = 0.75 \[ 2 \log{\left (x^{2} + 5 \right )} + \frac{21}{2 x^{2} + 10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x**3-x)/(x**2+5)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.219991, size = 34, normalized size = 1.7 \[ -\frac{4 \, x^{2} - 1}{2 \,{\left (x^{2} + 5\right )}} + 2 \,{\rm ln}\left (x^{2} + 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^3 - x)/(x^2 + 5)^2,x, algorithm="giac")
[Out]