Optimal. Leaf size=19 \[ \frac{x^8}{8 a \left (a+c x^4\right )^2} \]
[Out]
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Rubi [A] time = 0.0164148, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{x^8}{8 a \left (a+c x^4\right )^2} \]
Antiderivative was successfully verified.
[In] Int[x^7/(a + c*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 2.84427, size = 14, normalized size = 0.74 \[ \frac{x^{8}}{8 a \left (a + c x^{4}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**7/(c*x**4+a)**3,x)
[Out]
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Mathematica [A] time = 0.0164769, size = 24, normalized size = 1.26 \[ -\frac{a+2 c x^4}{8 c^2 \left (a+c x^4\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^7/(a + c*x^4)^3,x]
[Out]
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Maple [A] time = 0.013, size = 31, normalized size = 1.6 \[ -{\frac{1}{ \left ( 4\,c{x}^{4}+4\,a \right ){c}^{2}}}+{\frac{a}{8\,{c}^{2} \left ( c{x}^{4}+a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^7/(c*x^4+a)^3,x)
[Out]
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Maxima [A] time = 1.43852, size = 49, normalized size = 2.58 \[ -\frac{2 \, c x^{4} + a}{8 \,{\left (c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217046, size = 49, normalized size = 2.58 \[ -\frac{2 \, c x^{4} + a}{8 \,{\left (c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.81274, size = 36, normalized size = 1.89 \[ - \frac{a + 2 c x^{4}}{8 a^{2} c^{2} + 16 a c^{3} x^{4} + 8 c^{4} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**7/(c*x**4+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.220026, size = 30, normalized size = 1.58 \[ -\frac{2 \, c x^{4} + a}{8 \,{\left (c x^{4} + a\right )}^{2} c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^7/(c*x^4 + a)^3,x, algorithm="giac")
[Out]