Optimal. Leaf size=19 \[ \frac{x^{16}}{16 b \left (a x^8+b\right )^2} \]
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Rubi [A] time = 0.0057949, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {1593, 264} \[ \frac{x^{16}}{16 b \left (a x^8+b\right )^2} \]
Antiderivative was successfully verified.
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Rule 1593
Rule 264
Rubi steps
\begin{align*} \int \frac{1}{\left (\frac{b}{x^5}+a x^3\right )^3} \, dx &=\int \frac{x^{15}}{\left (b+a x^8\right )^3} \, dx\\ &=\frac{x^{16}}{16 b \left (b+a x^8\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0111089, size = 24, normalized size = 1.26 \[ -\frac{2 a x^8+b}{16 a^2 \left (a x^8+b\right )^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 31, normalized size = 1.6 \begin{align*}{\frac{b}{16\,{a}^{2} \left ( a{x}^{8}+b \right ) ^{2}}}-{\frac{1}{8\,{a}^{2} \left ( a{x}^{8}+b \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.10908, size = 49, normalized size = 2.58 \begin{align*} -\frac{2 \, a x^{8} + b}{16 \,{\left (a^{4} x^{16} + 2 \, a^{3} b x^{8} + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.820367, size = 76, normalized size = 4. \begin{align*} -\frac{2 \, a x^{8} + b}{16 \,{\left (a^{4} x^{16} + 2 \, a^{3} b x^{8} + a^{2} b^{2}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17288, size = 30, normalized size = 1.58 \begin{align*} -\frac{2 \, a x^{8} + b}{16 \,{\left (a x^{8} + b\right )}^{2} a^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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