Optimal. Leaf size=19 \[ -\frac {\left (a+b x^3\right )^9}{27 a x^{27}} \]
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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} \[ -\frac {\left (a+b x^3\right )^9}{27 a x^{27}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^8}{x^{28}} \, dx &=-\frac {\left (a+b x^3\right )^9}{27 a x^{27}}\\ \end {align*}
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Mathematica [B] time = 0.01, size = 108, normalized size = 5.68 \[ -\frac {a^8}{27 x^{27}}-\frac {a^7 b}{3 x^{24}}-\frac {4 a^6 b^2}{3 x^{21}}-\frac {28 a^5 b^3}{9 x^{18}}-\frac {14 a^4 b^4}{3 x^{15}}-\frac {14 a^3 b^5}{3 x^{12}}-\frac {28 a^2 b^6}{9 x^9}-\frac {4 a b^7}{3 x^6}-\frac {b^8}{3 x^3} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.76, size = 90, normalized size = 4.74 \[ -\frac {9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.20, size = 90, normalized size = 4.74 \[ -\frac {9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \]
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 \[ -\frac {b^{8}}{3 x^{3}}-\frac {4 a \,b^{7}}{3 x^{6}}-\frac {28 a^{2} b^{6}}{9 x^{9}}-\frac {14 a^{3} b^{5}}{3 x^{12}}-\frac {14 a^{4} b^{4}}{3 x^{15}}-\frac {28 a^{5} b^{3}}{9 x^{18}}-\frac {4 a^{6} b^{2}}{3 x^{21}}-\frac {a^{7} b}{3 x^{24}}-\frac {a^{8}}{27 x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.45, size = 90, normalized size = 4.74 \[ -\frac {9 \, b^{8} x^{24} + 36 \, a b^{7} x^{21} + 84 \, a^{2} b^{6} x^{18} + 126 \, a^{3} b^{5} x^{15} + 126 \, a^{4} b^{4} x^{12} + 84 \, a^{5} b^{3} x^{9} + 36 \, a^{6} b^{2} x^{6} + 9 \, a^{7} b x^{3} + a^{8}}{27 \, x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.23, size = 92, normalized size = 4.84 \[ -\frac {\frac {a^8}{27}+\frac {a^7\,b\,x^3}{3}+\frac {4\,a^6\,b^2\,x^6}{3}+\frac {28\,a^5\,b^3\,x^9}{9}+\frac {14\,a^4\,b^4\,x^{12}}{3}+\frac {14\,a^3\,b^5\,x^{15}}{3}+\frac {28\,a^2\,b^6\,x^{18}}{9}+\frac {4\,a\,b^7\,x^{21}}{3}+\frac {b^8\,x^{24}}{3}}{x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.65, size = 97, normalized size = 5.11 \[ \frac {- a^{8} - 9 a^{7} b x^{3} - 36 a^{6} b^{2} x^{6} - 84 a^{5} b^{3} x^{9} - 126 a^{4} b^{4} x^{12} - 126 a^{3} b^{5} x^{15} - 84 a^{2} b^{6} x^{18} - 36 a b^{7} x^{21} - 9 b^{8} x^{24}}{27 x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
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