Optimal. Leaf size=19 \[ -\frac{\left (a+b x^2\right )^9}{18 a x^{18}} \]
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Rubi [A] time = 0.0031426, 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} \[ -\frac{\left (a+b x^2\right )^9}{18 a x^{18}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^8}{x^{19}} \, dx &=-\frac{\left (a+b x^2\right )^9}{18 a x^{18}}\\ \end{align*}
Mathematica [B] time = 0.0045611, size = 100, normalized size = 5.26 \[ -\frac{2 a^6 b^2}{x^{14}}-\frac{14 a^5 b^3}{3 x^{12}}-\frac{7 a^4 b^4}{x^{10}}-\frac{7 a^3 b^5}{x^8}-\frac{14 a^2 b^6}{3 x^6}-\frac{a^7 b}{2 x^{16}}-\frac{a^8}{18 x^{18}}-\frac{2 a b^7}{x^4}-\frac{b^8}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.006, size = 91, normalized size = 4.8 \begin{align*} -7\,{\frac{{a}^{3}{b}^{5}}{{x}^{8}}}-7\,{\frac{{a}^{4}{b}^{4}}{{x}^{10}}}-2\,{\frac{a{b}^{7}}{{x}^{4}}}-{\frac{{a}^{8}}{18\,{x}^{18}}}-{\frac{14\,{a}^{5}{b}^{3}}{3\,{x}^{12}}}-{\frac{{b}^{8}}{2\,{x}^{2}}}-{\frac{14\,{a}^{2}{b}^{6}}{3\,{x}^{6}}}-2\,{\frac{{a}^{6}{b}^{2}}{{x}^{14}}}-{\frac{{a}^{7}b}{2\,{x}^{16}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 2.8204, size = 122, normalized size = 6.42 \begin{align*} -\frac{9 \, b^{8} x^{16} + 36 \, a b^{7} x^{14} + 84 \, a^{2} b^{6} x^{12} + 126 \, a^{3} b^{5} x^{10} + 126 \, a^{4} b^{4} x^{8} + 84 \, a^{5} b^{3} x^{6} + 36 \, a^{6} b^{2} x^{4} + 9 \, a^{7} b x^{2} + a^{8}}{18 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.23415, size = 203, normalized size = 10.68 \begin{align*} -\frac{9 \, b^{8} x^{16} + 36 \, a b^{7} x^{14} + 84 \, a^{2} b^{6} x^{12} + 126 \, a^{3} b^{5} x^{10} + 126 \, a^{4} b^{4} x^{8} + 84 \, a^{5} b^{3} x^{6} + 36 \, a^{6} b^{2} x^{4} + 9 \, a^{7} b x^{2} + a^{8}}{18 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.13006, size = 97, normalized size = 5.11 \begin{align*} - \frac{a^{8} + 9 a^{7} b x^{2} + 36 a^{6} b^{2} x^{4} + 84 a^{5} b^{3} x^{6} + 126 a^{4} b^{4} x^{8} + 126 a^{3} b^{5} x^{10} + 84 a^{2} b^{6} x^{12} + 36 a b^{7} x^{14} + 9 b^{8} x^{16}}{18 x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 2.09674, size = 122, normalized size = 6.42 \begin{align*} -\frac{9 \, b^{8} x^{16} + 36 \, a b^{7} x^{14} + 84 \, a^{2} b^{6} x^{12} + 126 \, a^{3} b^{5} x^{10} + 126 \, a^{4} b^{4} x^{8} + 84 \, a^{5} b^{3} x^{6} + 36 \, a^{6} b^{2} x^{4} + 9 \, a^{7} b x^{2} + a^{8}}{18 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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