Optimal. Leaf size=19 \[ -\frac{\left (a+b x^3\right )^6}{18 a x^{18}} \]
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Rubi [A] time = 0.0031309, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {264} \[ -\frac{\left (a+b x^3\right )^6}{18 a x^{18}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5}{x^{19}} \, dx &=-\frac{\left (a+b x^3\right )^6}{18 a x^{18}}\\ \end{align*}
Mathematica [B] time = 0.0042145, size = 69, normalized size = 3.63 \[ -\frac{5 a^3 b^2}{6 x^{12}}-\frac{10 a^2 b^3}{9 x^9}-\frac{a^4 b}{3 x^{15}}-\frac{a^5}{18 x^{18}}-\frac{5 a b^4}{6 x^6}-\frac{b^5}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.007, size = 58, normalized size = 3.1 \begin{align*} -{\frac{{b}^{5}}{3\,{x}^{3}}}-{\frac{{a}^{4}b}{3\,{x}^{15}}}-{\frac{5\,{a}^{3}{b}^{2}}{6\,{x}^{12}}}-{\frac{5\,a{b}^{4}}{6\,{x}^{6}}}-{\frac{{a}^{5}}{18\,{x}^{18}}}-{\frac{10\,{a}^{2}{b}^{3}}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.962189, size = 77, normalized size = 4.05 \begin{align*} -\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.65368, size = 128, normalized size = 6.74 \begin{align*} -\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.958493, size = 61, normalized size = 3.21 \begin{align*} - \frac{a^{5} + 6 a^{4} b x^{3} + 15 a^{3} b^{2} x^{6} + 20 a^{2} b^{3} x^{9} + 15 a b^{4} x^{12} + 6 b^{5} x^{15}}{18 x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.13228, size = 77, normalized size = 4.05 \begin{align*} -\frac{6 \, b^{5} x^{15} + 15 \, a b^{4} x^{12} + 20 \, a^{2} b^{3} x^{9} + 15 \, a^{3} b^{2} x^{6} + 6 \, a^{4} b x^{3} + a^{5}}{18 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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