Optimal. Leaf size=43 \[ -\frac{a^2 b}{5 x^{15}}-\frac{a^3}{18 x^{18}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]
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Rubi [A] time = 0.0184389, 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} \[ -\frac{a^2 b}{5 x^{15}}-\frac{a^3}{18 x^{18}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]
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^{19}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^7} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (\frac{a^3}{x^7}+\frac{3 a^2 b}{x^6}+\frac{3 a b^2}{x^5}+\frac{b^3}{x^4}\right ) \, dx,x,x^3\right )\\ &=-\frac{a^3}{18 x^{18}}-\frac{a^2 b}{5 x^{15}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9}\\ \end{align*}
Mathematica [A] time = 0.0037339, size = 43, normalized size = 1. \[ -\frac{a^2 b}{5 x^{15}}-\frac{a^3}{18 x^{18}}-\frac{a b^2}{4 x^{12}}-\frac{b^3}{9 x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{{a}^{3}}{18\,{x}^{18}}}-{\frac{{a}^{2}b}{5\,{x}^{15}}}-{\frac{a{b}^{2}}{4\,{x}^{12}}}-{\frac{{b}^{3}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.97121, size = 50, normalized size = 1.16 \begin{align*} -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66253, size = 88, normalized size = 2.05 \begin{align*} -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.713632, size = 39, normalized size = 0.91 \begin{align*} - \frac{10 a^{3} + 36 a^{2} b x^{3} + 45 a b^{2} x^{6} + 20 b^{3} x^{9}}{180 x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10448, size = 50, normalized size = 1.16 \begin{align*} -\frac{20 \, b^{3} x^{9} + 45 \, a b^{2} x^{6} + 36 \, a^{2} b x^{3} + 10 \, a^{3}}{180 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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