Optimal. Leaf size=22 \[ \frac{\log (x)}{b}-\frac{\log \left (b+c x^2\right )}{2 b} \]
[Out]
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Rubi [A] time = 0.038038, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{\log (x)}{b}-\frac{\log \left (b+c x^2\right )}{2 b} \]
Antiderivative was successfully verified.
[In] Int[x/(b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [A] time = 8.41414, size = 19, normalized size = 0.86 \[ \frac{\log{\left (x^{2} \right )}}{2 b} - \frac{\log{\left (b + c x^{2} \right )}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(c*x**4+b*x**2),x)
[Out]
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Mathematica [A] time = 0.00836916, size = 22, normalized size = 1. \[ \frac{\log (x)}{b}-\frac{\log \left (b+c x^2\right )}{2 b} \]
Antiderivative was successfully verified.
[In] Integrate[x/(b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0.007, size = 21, normalized size = 1. \[{\frac{\ln \left ( x \right ) }{b}}-{\frac{\ln \left ( c{x}^{2}+b \right ) }{2\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(c*x^4+b*x^2),x)
[Out]
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Maxima [A] time = 0.680484, size = 31, normalized size = 1.41 \[ -\frac{\log \left (c x^{2} + b\right )}{2 \, b} + \frac{\log \left (x^{2}\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(c*x^4 + b*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.255674, size = 24, normalized size = 1.09 \[ -\frac{\log \left (c x^{2} + b\right ) - 2 \, \log \left (x\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(c*x^4 + b*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.505183, size = 15, normalized size = 0.68 \[ \frac{\log{\left (x \right )}}{b} - \frac{\log{\left (\frac{b}{c} + x^{2} \right )}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(c*x**4+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.271004, size = 30, normalized size = 1.36 \[ -\frac{{\rm ln}\left ({\left | c x^{2} + b \right |}\right )}{2 \, b} + \frac{{\rm ln}\left ({\left | x \right |}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(c*x^4 + b*x^2),x, algorithm="giac")
[Out]