Optimal. Leaf size=15 \[ \frac{\log \left (b+c x^2\right )}{2 c} \]
[Out]
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Rubi [A] time = 0.0197065, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{\log \left (b+c x^2\right )}{2 c} \]
Antiderivative was successfully verified.
[In] Int[x^3/(b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [A] time = 4.18605, size = 10, normalized size = 0.67 \[ \frac{\log{\left (b + c x^{2} \right )}}{2 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(c*x**4+b*x**2),x)
[Out]
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Mathematica [A] time = 0.0034123, size = 15, normalized size = 1. \[ \frac{\log \left (b+c x^2\right )}{2 c} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0.002, size = 14, normalized size = 0.9 \[{\frac{\ln \left ( c{x}^{2}+b \right ) }{2\,c}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(c*x^4+b*x^2),x)
[Out]
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Maxima [A] time = 0.688025, size = 18, normalized size = 1.2 \[ \frac{\log \left (c x^{2} + b\right )}{2 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(c*x^4 + b*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.250013, size = 18, normalized size = 1.2 \[ \frac{\log \left (c x^{2} + b\right )}{2 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(c*x^4 + b*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.237187, size = 10, normalized size = 0.67 \[ \frac{\log{\left (b + c x^{2} \right )}}{2 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(c*x**4+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.270813, size = 19, normalized size = 1.27 \[ \frac{{\rm ln}\left ({\left | c x^{2} + b \right |}\right )}{2 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(c*x^4 + b*x^2),x, algorithm="giac")
[Out]