Optimal. Leaf size=24 \[ -\frac {x^{-9 n} \left (a+b x^n\right )^9}{9 a n} \]
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Rubi [A] time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {264} \[ -\frac {x^{-9 n} \left (a+b x^n\right )^9}{9 a n} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int x^{-1-9 n} \left (a+b x^n\right )^8 \, dx &=-\frac {x^{-9 n} \left (a+b x^n\right )^9}{9 a n}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.00 \[ -\frac {x^{-9 n} \left (a+b x^n\right )^9}{9 a n} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.60, size = 111, normalized size = 4.62 \[ -\frac {9 \, b^{8} x^{8 \, n} + 36 \, a b^{7} x^{7 \, n} + 84 \, a^{2} b^{6} x^{6 \, n} + 126 \, a^{3} b^{5} x^{5 \, n} + 126 \, a^{4} b^{4} x^{4 \, n} + 84 \, a^{5} b^{3} x^{3 \, n} + 36 \, a^{6} b^{2} x^{2 \, n} + 9 \, a^{7} b x^{n} + a^{8}}{9 \, n x^{9 \, n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.29, size = 111, normalized size = 4.62 \[ -\frac {9 \, b^{8} x^{8 \, n} + 36 \, a b^{7} x^{7 \, n} + 84 \, a^{2} b^{6} x^{6 \, n} + 126 \, a^{3} b^{5} x^{5 \, n} + 126 \, a^{4} b^{4} x^{4 \, n} + 84 \, a^{5} b^{3} x^{3 \, n} + 36 \, a^{6} b^{2} x^{2 \, n} + 9 \, a^{7} b x^{n} + a^{8}}{9 \, n x^{9 \, n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 136, normalized size = 5.67 \[ -\frac {a^{8} x^{-9 n}}{9 n}-\frac {a^{7} b \,x^{-8 n}}{n}-\frac {4 a^{6} b^{2} x^{-7 n}}{n}-\frac {28 a^{5} b^{3} x^{-6 n}}{3 n}-\frac {14 a^{4} b^{4} x^{-5 n}}{n}-\frac {14 a^{3} b^{5} x^{-4 n}}{n}-\frac {28 a^{2} b^{6} x^{-3 n}}{3 n}-\frac {4 a \,b^{7} x^{-2 n}}{n}-\frac {b^{8} x^{-n}}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 151, normalized size = 6.29 \[ -\frac {a^{8}}{9 \, n x^{9 \, n}} - \frac {a^{7} b}{n x^{8 \, n}} - \frac {4 \, a^{6} b^{2}}{n x^{7 \, n}} - \frac {28 \, a^{5} b^{3}}{3 \, n x^{6 \, n}} - \frac {14 \, a^{4} b^{4}}{n x^{5 \, n}} - \frac {14 \, a^{3} b^{5}}{n x^{4 \, n}} - \frac {28 \, a^{2} b^{6}}{3 \, n x^{3 \, n}} - \frac {4 \, a b^{7}}{n x^{2 \, n}} - \frac {b^{8}}{n x^{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 151, normalized size = 6.29 \[ -\frac {a^8}{9\,n\,x^{9\,n}}-\frac {b^8}{n\,x^n}-\frac {28\,a^2\,b^6}{3\,n\,x^{3\,n}}-\frac {14\,a^3\,b^5}{n\,x^{4\,n}}-\frac {14\,a^4\,b^4}{n\,x^{5\,n}}-\frac {28\,a^5\,b^3}{3\,n\,x^{6\,n}}-\frac {4\,a^6\,b^2}{n\,x^{7\,n}}-\frac {4\,a\,b^7}{n\,x^{2\,n}}-\frac {a^7\,b}{n\,x^{8\,n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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