Optimal. Leaf size=19 \[ \frac {x^{16}}{16 b \left (a x^8+b\right )^2} \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {x^{16}}{16 b \left (a x^8+b\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 264
Rule 1593
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*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.26 \begin {gather*} -\frac {2 a x^8+b}{16 a^2 \left (a x^8+b\right )^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (\frac {b}{x^5}+a x^3\right )^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.38, size = 36, normalized size = 1.89 \begin {gather*} -\frac {2 \, a x^{8} + b}{16 \, {\left (a^{4} x^{16} + 2 \, a^{3} b x^{8} + a^{2} b^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 22, normalized size = 1.16 \begin {gather*} -\frac {2 \, a x^{8} + b}{16 \, {\left (a x^{8} + b\right )}^{2} a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 31, normalized size = 1.63 \begin {gather*} \frac {b}{16 \left (a \,x^{8}+b \right )^{2} a^{2}}-\frac {1}{8 \left (a \,x^{8}+b \right ) a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.31, size = 36, normalized size = 1.89 \begin {gather*} -\frac {2 \, a x^{8} + b}{16 \, {\left (a^{4} x^{16} + 2 \, a^{3} b x^{8} + a^{2} b^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.18, size = 37, normalized size = 1.95 \begin {gather*} -\frac {\frac {b}{16\,a^2}+\frac {x^8}{8\,a}}{a^2\,x^{16}+2\,a\,b\,x^8+b^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.74, size = 36, normalized size = 1.89 \begin {gather*} \frac {- 2 a x^{8} - b}{16 a^{4} x^{16} + 32 a^{3} b x^{8} + 16 a^{2} b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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