Optimal. Leaf size=40 \[ \frac{b^2 \log \left (b+c x^2\right )}{2 c^3}-\frac{b x^2}{2 c^2}+\frac{x^4}{4 c} \]
[Out]
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Rubi [A] time = 0.0743586, antiderivative size = 40, 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 \[ \frac{b^2 \log \left (b+c x^2\right )}{2 c^3}-\frac{b x^2}{2 c^2}+\frac{x^4}{4 c} \]
Antiderivative was successfully verified.
[In] Int[x^7/(b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b^{2} \log{\left (b + c x^{2} \right )}}{2 c^{3}} + \frac{\int ^{x^{2}} x\, dx}{2 c} - \frac{\int ^{x^{2}} b\, dx}{2 c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(c*x**4+b*x**2),x)
[Out]
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Mathematica [A] time = 0.0093579, size = 40, normalized size = 1. \[ \frac{b^2 \log \left (b+c x^2\right )}{2 c^3}-\frac{b x^2}{2 c^2}+\frac{x^4}{4 c} \]
Antiderivative was successfully verified.
[In] Integrate[x^7/(b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0.004, size = 35, normalized size = 0.9 \[ -{\frac{b{x}^{2}}{2\,{c}^{2}}}+{\frac{{x}^{4}}{4\,c}}+{\frac{{b}^{2}\ln \left ( c{x}^{2}+b \right ) }{2\,{c}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(c*x^4+b*x^2),x)
[Out]
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Maxima [A] time = 0.688344, size = 46, normalized size = 1.15 \[ \frac{b^{2} \log \left (c x^{2} + b\right )}{2 \, c^{3}} + \frac{c x^{4} - 2 \, b x^{2}}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + b*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.251709, size = 45, normalized size = 1.12 \[ \frac{c^{2} x^{4} - 2 \, b c x^{2} + 2 \, b^{2} \log \left (c x^{2} + b\right )}{4 \, c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + b*x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.2139, size = 32, normalized size = 0.8 \[ \frac{b^{2} \log{\left (b + c x^{2} \right )}}{2 c^{3}} - \frac{b x^{2}}{2 c^{2}} + \frac{x^{4}}{4 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(c*x**4+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.270056, size = 47, normalized size = 1.18 \[ \frac{b^{2}{\rm ln}\left ({\left | c x^{2} + b \right |}\right )}{2 \, c^{3}} + \frac{c x^{4} - 2 \, b x^{2}}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + b*x^2),x, algorithm="giac")
[Out]