Optimal. Leaf size=19 \[ \frac {x^8}{8 a \left (a+c x^4\right )^2} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [B] time = 0.55, size = 36, normalized size = 1.89 \[ -\frac {2 \, c x^{4} + a}{8 \, {\left (c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 22, normalized size = 1.16 \[ -\frac {2 \, c x^{4} + a}{8 \, {\left (c x^{4} + a\right )}^{2} c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 31, normalized size = 1.63 \[ \frac {a}{8 \left (c \,x^{4}+a \right )^{2} c^{2}}-\frac {1}{4 \left (c \,x^{4}+a \right ) c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.32, size = 36, normalized size = 1.89 \[ -\frac {2 \, c x^{4} + a}{8 \, {\left (c^{4} x^{8} + 2 \, a c^{3} x^{4} + a^{2} c^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 1.95 \[ -\frac {\frac {a}{8\,c^2}+\frac {x^4}{4\,c}}{a^2+2\,a\,c\,x^4+c^2\,x^8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.50, 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.
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