Optimal. Leaf size=27 \[ \frac{x^4}{4 c}-\frac{a \log \left (a+c x^4\right )}{4 c^2} \]
[Out]
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Rubi [A] time = 0.0465332, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{x^4}{4 c}-\frac{a \log \left (a+c x^4\right )}{4 c^2} \]
Antiderivative was successfully verified.
[In] Int[x^7/(a + c*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a \log{\left (a + c x^{4} \right )}}{4 c^{2}} + \frac{\int ^{x^{4}} \frac{1}{c}\, dx}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(c*x**4+a),x)
[Out]
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Mathematica [A] time = 0.0104449, size = 27, normalized size = 1. \[ \frac{x^4}{4 c}-\frac{a \log \left (a+c x^4\right )}{4 c^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^7/(a + c*x^4),x]
[Out]
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Maple [A] time = 0.004, size = 24, normalized size = 0.9 \[{\frac{{x}^{4}}{4\,c}}-{\frac{a\ln \left ( c{x}^{4}+a \right ) }{4\,{c}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(c*x^4+a),x)
[Out]
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Maxima [A] time = 1.43794, size = 31, normalized size = 1.15 \[ \frac{x^{4}}{4 \, c} - \frac{a \log \left (c x^{4} + a\right )}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22011, size = 30, normalized size = 1.11 \[ \frac{c x^{4} - a \log \left (c x^{4} + a\right )}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.33632, size = 20, normalized size = 0.74 \[ - \frac{a \log{\left (a + c x^{4} \right )}}{4 c^{2}} + \frac{x^{4}}{4 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(c*x**4+a),x)
[Out]
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GIAC/XCAS [A] time = 0.221271, size = 32, normalized size = 1.19 \[ \frac{x^{4}}{4 \, c} - \frac{a{\rm ln}\left ({\left | c x^{4} + a \right |}\right )}{4 \, c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + a),x, algorithm="giac")
[Out]