Optimal. Leaf size=19 \[ \frac{x^8}{8 a \left (a+c x^4\right )^2} \]
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Rubi [A] time = 0.0035922, 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, Rules used = {264} \[ \frac{x^8}{8 a \left (a+c x^4\right )^2} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{x^7}{\left (a+c x^4\right )^3} \, dx &=\frac{x^8}{8 a \left (a+c x^4\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0087713, 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.
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Maple [A] time = 0.01, size = 31, normalized size = 1.6 \begin{align*} -{\frac{1}{4\,{c}^{2} \left ( c{x}^{4}+a \right ) }}+{\frac{a}{8\,{c}^{2} \left ( c{x}^{4}+a \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.985189, size = 49, normalized size = 2.58 \begin{align*} -\frac{2 \, c x^{4} + a}{8 \,{\left (c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.64476, size = 73, normalized size = 3.84 \begin{align*} -\frac{2 \, c x^{4} + a}{8 \,{\left (c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.40093, size = 36, normalized size = 1.89 \begin{align*} - \frac{a + 2 c x^{4}}{8 a^{2} c^{2} + 16 a c^{3} x^{4} + 8 c^{4} x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11741, size = 30, normalized size = 1.58 \begin{align*} -\frac{2 \, c x^{4} + a}{8 \,{\left (c x^{4} + a\right )}^{2} c^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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