Optimal. Leaf size=40 \[ \frac{b \left (a+b x^3\right )^4}{60 a^2 x^{12}}-\frac{\left (a+b x^3\right )^4}{15 a x^{15}} \]
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Rubi [A] time = 0.0166418, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231, Rules used = {266, 45, 37} \[ \frac{b \left (a+b x^3\right )^4}{60 a^2 x^{12}}-\frac{\left (a+b x^3\right )^4}{15 a x^{15}} \]
Antiderivative was successfully verified.
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Rule 266
Rule 45
Rule 37
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^3}{x^{16}} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^6} \, dx,x,x^3\right )\\ &=-\frac{\left (a+b x^3\right )^4}{15 a x^{15}}-\frac{b \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^5} \, dx,x,x^3\right )}{15 a}\\ &=-\frac{\left (a+b x^3\right )^4}{15 a x^{15}}+\frac{b \left (a+b x^3\right )^4}{60 a^2 x^{12}}\\ \end{align*}
Mathematica [A] time = 0.0036505, size = 43, normalized size = 1.08 \[ -\frac{a^2 b}{4 x^{12}}-\frac{a^3}{15 x^{15}}-\frac{a b^2}{3 x^9}-\frac{b^3}{6 x^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 36, normalized size = 0.9 \begin{align*} -{\frac{{a}^{3}}{15\,{x}^{15}}}-{\frac{{a}^{2}b}{4\,{x}^{12}}}-{\frac{{b}^{3}}{6\,{x}^{6}}}-{\frac{a{b}^{2}}{3\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959549, size = 50, normalized size = 1.25 \begin{align*} -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66335, size = 85, normalized size = 2.12 \begin{align*} -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.666657, size = 39, normalized size = 0.98 \begin{align*} - \frac{4 a^{3} + 15 a^{2} b x^{3} + 20 a b^{2} x^{6} + 10 b^{3} x^{9}}{60 x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13066, size = 50, normalized size = 1.25 \begin{align*} -\frac{10 \, b^{3} x^{9} + 20 \, a b^{2} x^{6} + 15 \, a^{2} b x^{3} + 4 \, a^{3}}{60 \, x^{15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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