Optimal. Leaf size=19 \[ \frac {x^{10}}{10 b \left (a x^5+b\right )^2} \]
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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^{10}}{10 b \left (a x^5+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^3}+a x^2\right )^3} \, dx &=\int \frac {x^9}{\left (b+a x^5\right )^3} \, dx\\ &=\frac {x^{10}}{10 b \left (b+a x^5\right )^2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 24, normalized size = 1.26 \begin {gather*} -\frac {2 a x^5+b}{10 a^2 \left (a x^5+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^3}+a x^2\right )^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.37, size = 36, normalized size = 1.89 \begin {gather*} -\frac {2 \, a x^{5} + b}{10 \, {\left (a^{4} x^{10} + 2 \, a^{3} b x^{5} + a^{2} b^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 22, normalized size = 1.16 \begin {gather*} -\frac {2 \, a x^{5} + b}{10 \, {\left (a x^{5} + b\right )}^{2} a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 31, normalized size = 1.63 \begin {gather*} \frac {b}{10 \left (a \,x^{5}+b \right )^{2} a^{2}}-\frac {1}{5 \left (a \,x^{5}+b \right ) a^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.29, size = 36, normalized size = 1.89 \begin {gather*} -\frac {2 \, a x^{5} + b}{10 \, {\left (a^{4} x^{10} + 2 \, a^{3} b x^{5} + a^{2} b^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 37, normalized size = 1.95 \begin {gather*} -\frac {\frac {b}{10\,a^2}+\frac {x^5}{5\,a}}{a^2\,x^{10}+2\,a\,b\,x^5+b^2} \end {gather*}
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 \begin {gather*} \frac {- 2 a x^{5} - b}{10 a^{4} x^{10} + 20 a^{3} b x^{5} + 10 a^{2} b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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