Optimal. Leaf size=40 \[ \frac {b \left (a+b x^3\right )^9}{270 a^2 x^{27}}-\frac {\left (a+b x^3\right )^9}{30 a x^{30}} \]
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Rubi [A] time = 0.02, antiderivative size = 40, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.231, Rules used = {266, 45, 37} \[ \frac {b \left (a+b x^3\right )^9}{270 a^2 x^{27}}-\frac {\left (a+b x^3\right )^9}{30 a x^{30}} \]
Antiderivative was successfully verified.
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Rule 37
Rule 45
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^8}{x^{31}} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {(a+b x)^8}{x^{11}} \, dx,x,x^3\right )\\ &=-\frac {\left (a+b x^3\right )^9}{30 a x^{30}}-\frac {b \operatorname {Subst}\left (\int \frac {(a+b x)^8}{x^{10}} \, dx,x,x^3\right )}{30 a}\\ &=-\frac {\left (a+b x^3\right )^9}{30 a x^{30}}+\frac {b \left (a+b x^3\right )^9}{270 a^2 x^{27}}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 108, normalized size = 2.70 \[ -\frac {a^8}{30 x^{30}}-\frac {8 a^7 b}{27 x^{27}}-\frac {7 a^6 b^2}{6 x^{24}}-\frac {8 a^5 b^3}{3 x^{21}}-\frac {35 a^4 b^4}{9 x^{18}}-\frac {56 a^3 b^5}{15 x^{15}}-\frac {7 a^2 b^6}{3 x^{12}}-\frac {8 a b^7}{9 x^9}-\frac {b^8}{6 x^6} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.63, size = 92, normalized size = 2.30 \[ -\frac {45 \, b^{8} x^{24} + 240 \, a b^{7} x^{21} + 630 \, a^{2} b^{6} x^{18} + 1008 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 720 \, a^{5} b^{3} x^{9} + 315 \, a^{6} b^{2} x^{6} + 80 \, a^{7} b x^{3} + 9 \, a^{8}}{270 \, x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 92, normalized size = 2.30 \[ -\frac {45 \, b^{8} x^{24} + 240 \, a b^{7} x^{21} + 630 \, a^{2} b^{6} x^{18} + 1008 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 720 \, a^{5} b^{3} x^{9} + 315 \, a^{6} b^{2} x^{6} + 80 \, a^{7} b x^{3} + 9 \, a^{8}}{270 \, x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 91, normalized size = 2.28 \[ -\frac {b^{8}}{6 x^{6}}-\frac {8 a \,b^{7}}{9 x^{9}}-\frac {7 a^{2} b^{6}}{3 x^{12}}-\frac {56 a^{3} b^{5}}{15 x^{15}}-\frac {35 a^{4} b^{4}}{9 x^{18}}-\frac {8 a^{5} b^{3}}{3 x^{21}}-\frac {7 a^{6} b^{2}}{6 x^{24}}-\frac {8 a^{7} b}{27 x^{27}}-\frac {a^{8}}{30 x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.29, size = 92, normalized size = 2.30 \[ -\frac {45 \, b^{8} x^{24} + 240 \, a b^{7} x^{21} + 630 \, a^{2} b^{6} x^{18} + 1008 \, a^{3} b^{5} x^{15} + 1050 \, a^{4} b^{4} x^{12} + 720 \, a^{5} b^{3} x^{9} + 315 \, a^{6} b^{2} x^{6} + 80 \, a^{7} b x^{3} + 9 \, a^{8}}{270 \, x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.98, size = 92, normalized size = 2.30 \[ -\frac {\frac {a^8}{30}+\frac {8\,a^7\,b\,x^3}{27}+\frac {7\,a^6\,b^2\,x^6}{6}+\frac {8\,a^5\,b^3\,x^9}{3}+\frac {35\,a^4\,b^4\,x^{12}}{9}+\frac {56\,a^3\,b^5\,x^{15}}{15}+\frac {7\,a^2\,b^6\,x^{18}}{3}+\frac {8\,a\,b^7\,x^{21}}{9}+\frac {b^8\,x^{24}}{6}}{x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.36, size = 99, normalized size = 2.48 \[ \frac {- 9 a^{8} - 80 a^{7} b x^{3} - 315 a^{6} b^{2} x^{6} - 720 a^{5} b^{3} x^{9} - 1050 a^{4} b^{4} x^{12} - 1008 a^{3} b^{5} x^{15} - 630 a^{2} b^{6} x^{18} - 240 a b^{7} x^{21} - 45 b^{8} x^{24}}{270 x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
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