Optimal. Leaf size=43 \[ -\frac{a^2 b}{6 x^{18}}-\frac{a^3}{21 x^{21}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]
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Rubi [A] time = 0.0185465, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ -\frac{a^2 b}{6 x^{18}}-\frac{a^3}{21 x^{21}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^3}{x^{22}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^8} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^3}{x^8}+\frac{3 a^2 b}{x^7}+\frac{3 a b^2}{x^6}+\frac{b^3}{x^5}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^3}{21 x^{21}}-\frac{a^2 b}{6 x^{18}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}}\\ \end{align*}
Mathematica [A] time = 0.0037663, size = 43, normalized size = 1. \[ -\frac{a^2 b}{6 x^{18}}-\frac{a^3}{21 x^{21}}-\frac{a b^2}{5 x^{15}}-\frac{b^3}{12 x^{12}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{21\,{x}^{21}}}-{\frac{{a}^{2}b}{6\,{x}^{18}}}-{\frac{a{b}^{2}}{5\,{x}^{15}}}-{\frac{{b}^{3}}{12\,{x}^{12}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.99636, size = 50, normalized size = 1.16 \begin{align*} -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72042, size = 88, normalized size = 2.05 \begin{align*} -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.775907, size = 39, normalized size = 0.91 \begin{align*} - \frac{20 a^{3} + 70 a^{2} b x^{3} + 84 a b^{2} x^{6} + 35 b^{3} x^{9}}{420 x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13253, size = 50, normalized size = 1.16 \begin{align*} -\frac{35 \, b^{3} x^{9} + 84 \, a b^{2} x^{6} + 70 \, a^{2} b x^{3} + 20 \, a^{3}}{420 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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