Optimal. Leaf size=52 \[ -\frac{a^2}{8 c^3 \left (a+c x^4\right )^2}+\frac{a}{2 c^3 \left (a+c x^4\right )}+\frac{\log \left (a+c x^4\right )}{4 c^3} \]
[Out]
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Rubi [A] time = 0.0832737, antiderivative size = 52, 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 \[ -\frac{a^2}{8 c^3 \left (a+c x^4\right )^2}+\frac{a}{2 c^3 \left (a+c x^4\right )}+\frac{\log \left (a+c x^4\right )}{4 c^3} \]
Antiderivative was successfully verified.
[In] Int[x^11/(a + c*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 11.6202, size = 42, normalized size = 0.81 \[ - \frac{a^{2}}{8 c^{3} \left (a + c x^{4}\right )^{2}} + \frac{a}{2 c^{3} \left (a + c x^{4}\right )} + \frac{\log{\left (a + c x^{4} \right )}}{4 c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(c*x**4+a)**3,x)
[Out]
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Mathematica [A] time = 0.0324476, size = 39, normalized size = 0.75 \[ \frac{\frac{a \left (3 a+4 c x^4\right )}{\left (a+c x^4\right )^2}+2 \log \left (a+c x^4\right )}{8 c^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(a + c*x^4)^3,x]
[Out]
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Maple [A] time = 0.016, size = 47, normalized size = 0.9 \[ -{\frac{{a}^{2}}{8\,{c}^{3} \left ( c{x}^{4}+a \right ) ^{2}}}+{\frac{a}{2\,{c}^{3} \left ( c{x}^{4}+a \right ) }}+{\frac{\ln \left ( c{x}^{4}+a \right ) }{4\,{c}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(c*x^4+a)^3,x)
[Out]
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Maxima [A] time = 1.45577, size = 74, normalized size = 1.42 \[ \frac{4 \, a c x^{4} + 3 \, a^{2}}{8 \,{\left (c^{5} x^{8} + 2 \, a c^{4} x^{4} + a^{2} c^{3}\right )}} + \frac{\log \left (c x^{4} + a\right )}{4 \, c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(c*x^4 + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218644, size = 93, normalized size = 1.79 \[ \frac{4 \, a c x^{4} + 3 \, a^{2} + 2 \,{\left (c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right )} \log \left (c x^{4} + a\right )}{8 \,{\left (c^{5} x^{8} + 2 \, a c^{4} x^{4} + a^{2} c^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(c*x^4 + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.03825, size = 53, normalized size = 1.02 \[ \frac{3 a^{2} + 4 a c x^{4}}{8 a^{2} c^{3} + 16 a c^{4} x^{4} + 8 c^{5} x^{8}} + \frac{\log{\left (a + c x^{4} \right )}}{4 c^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(c*x**4+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.226214, size = 57, normalized size = 1.1 \[ \frac{{\rm ln}\left ({\left | c x^{4} + a \right |}\right )}{4 \, c^{3}} - \frac{3 \, c x^{8} + 2 \, a x^{4}}{8 \,{\left (c x^{4} + a\right )}^{2} c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(c*x^4 + a)^3,x, algorithm="giac")
[Out]