Optimal. Leaf size=69 \[ -\frac{5 a^3 b^2}{7 x^{14}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{5 a^4 b}{16 x^{16}}-\frac{a^5}{18 x^{18}}-\frac{a b^4}{2 x^{10}}-\frac{b^5}{8 x^8} \]
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Rubi [A] time = 0.0316203, antiderivative size = 69, 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} \[ -\frac{5 a^3 b^2}{7 x^{14}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{5 a^4 b}{16 x^{16}}-\frac{a^5}{18 x^{18}}-\frac{a b^4}{2 x^{10}}-\frac{b^5}{8 x^8} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^2\right )^5}{x^{19}} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x^{10}} \, dx,x,x^2\right )\\ &=\frac{1}{2} \operatorname{Subst}\left (\int \left (\frac{a^5}{x^{10}}+\frac{5 a^4 b}{x^9}+\frac{10 a^3 b^2}{x^8}+\frac{10 a^2 b^3}{x^7}+\frac{5 a b^4}{x^6}+\frac{b^5}{x^5}\right ) \, dx,x,x^2\right )\\ &=-\frac{a^5}{18 x^{18}}-\frac{5 a^4 b}{16 x^{16}}-\frac{5 a^3 b^2}{7 x^{14}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{a b^4}{2 x^{10}}-\frac{b^5}{8 x^8}\\ \end{align*}
Mathematica [A] time = 0.0040041, size = 69, normalized size = 1. \[ -\frac{5 a^3 b^2}{7 x^{14}}-\frac{5 a^2 b^3}{6 x^{12}}-\frac{5 a^4 b}{16 x^{16}}-\frac{a^5}{18 x^{18}}-\frac{a b^4}{2 x^{10}}-\frac{b^5}{8 x^8} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 58, normalized size = 0.8 \begin{align*} -{\frac{{a}^{5}}{18\,{x}^{18}}}-{\frac{5\,{a}^{4}b}{16\,{x}^{16}}}-{\frac{5\,{a}^{3}{b}^{2}}{7\,{x}^{14}}}-{\frac{5\,{a}^{2}{b}^{3}}{6\,{x}^{12}}}-{\frac{a{b}^{4}}{2\,{x}^{10}}}-{\frac{{b}^{5}}{8\,{x}^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.14467, size = 80, normalized size = 1.16 \begin{align*} -\frac{126 \, b^{5} x^{10} + 504 \, a b^{4} x^{8} + 840 \, a^{2} b^{3} x^{6} + 720 \, a^{3} b^{2} x^{4} + 315 \, a^{4} b x^{2} + 56 \, a^{5}}{1008 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.22489, size = 143, normalized size = 2.07 \begin{align*} -\frac{126 \, b^{5} x^{10} + 504 \, a b^{4} x^{8} + 840 \, a^{2} b^{3} x^{6} + 720 \, a^{3} b^{2} x^{4} + 315 \, a^{4} b x^{2} + 56 \, a^{5}}{1008 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.772806, size = 63, normalized size = 0.91 \begin{align*} - \frac{56 a^{5} + 315 a^{4} b x^{2} + 720 a^{3} b^{2} x^{4} + 840 a^{2} b^{3} x^{6} + 504 a b^{4} x^{8} + 126 b^{5} x^{10}}{1008 x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.60327, size = 80, normalized size = 1.16 \begin{align*} -\frac{126 \, b^{5} x^{10} + 504 \, a b^{4} x^{8} + 840 \, a^{2} b^{3} x^{6} + 720 \, a^{3} b^{2} x^{4} + 315 \, a^{4} b x^{2} + 56 \, a^{5}}{1008 \, x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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