Optimal. Leaf size=19 \[ -\frac {\left (a+b x^2\right )^9}{18 a x^{18}} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, 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*}
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Mathematica [B] time = 0.00, size = 100, normalized size = 5.26 \[ -\frac {a^8}{18 x^{18}}-\frac {a^7 b}{2 x^{16}}-\frac {2 a^6 b^2}{x^{14}}-\frac {14 a^5 b^3}{3 x^{12}}-\frac {7 a^4 b^4}{x^{10}}-\frac {7 a^3 b^5}{x^8}-\frac {14 a^2 b^6}{3 x^6}-\frac {2 a b^7}{x^4}-\frac {b^8}{2 x^2} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.79, size = 90, normalized size = 4.74 \[ -\frac {9 \, b^{8} x^{16} + 36 \, a b^{7} x^{14} + 84 \, a^{2} b^{6} x^{12} + 126 \, a^{3} b^{5} x^{10} + 126 \, a^{4} b^{4} x^{8} + 84 \, a^{5} b^{3} x^{6} + 36 \, a^{6} b^{2} x^{4} + 9 \, a^{7} b x^{2} + a^{8}}{18 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.07, size = 90, normalized size = 4.74 \[ -\frac {9 \, b^{8} x^{16} + 36 \, a b^{7} x^{14} + 84 \, a^{2} b^{6} x^{12} + 126 \, a^{3} b^{5} x^{10} + 126 \, a^{4} b^{4} x^{8} + 84 \, a^{5} b^{3} x^{6} + 36 \, a^{6} b^{2} x^{4} + 9 \, a^{7} b x^{2} + a^{8}}{18 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 91, normalized size = 4.79 \[ -\frac {b^{8}}{2 x^{2}}-\frac {2 a \,b^{7}}{x^{4}}-\frac {14 a^{2} b^{6}}{3 x^{6}}-\frac {7 a^{3} b^{5}}{x^{8}}-\frac {7 a^{4} b^{4}}{x^{10}}-\frac {14 a^{5} b^{3}}{3 x^{12}}-\frac {2 a^{6} b^{2}}{x^{14}}-\frac {a^{7} b}{2 x^{16}}-\frac {a^{8}}{18 x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.32, size = 90, normalized size = 4.74 \[ -\frac {9 \, b^{8} x^{16} + 36 \, a b^{7} x^{14} + 84 \, a^{2} b^{6} x^{12} + 126 \, a^{3} b^{5} x^{10} + 126 \, a^{4} b^{4} x^{8} + 84 \, a^{5} b^{3} x^{6} + 36 \, a^{6} b^{2} x^{4} + 9 \, a^{7} b x^{2} + a^{8}}{18 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 92, normalized size = 4.84 \[ -\frac {\frac {a^8}{18}+\frac {a^7\,b\,x^2}{2}+2\,a^6\,b^2\,x^4+\frac {14\,a^5\,b^3\,x^6}{3}+7\,a^4\,b^4\,x^8+7\,a^3\,b^5\,x^{10}+\frac {14\,a^2\,b^6\,x^{12}}{3}+2\,a\,b^7\,x^{14}+\frac {b^8\,x^{16}}{2}}{x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.90, size = 97, normalized size = 5.11 \[ \frac {- a^{8} - 9 a^{7} b x^{2} - 36 a^{6} b^{2} x^{4} - 84 a^{5} b^{3} x^{6} - 126 a^{4} b^{4} x^{8} - 126 a^{3} b^{5} x^{10} - 84 a^{2} b^{6} x^{12} - 36 a b^{7} x^{14} - 9 b^{8} x^{16}}{18 x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
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