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 = 0.0058193, antiderivative size = 24, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0103317, size = 24, normalized size = 1. \[ -\frac{x^{-9 n} \left (a+b x^n\right )^9}{9 a n} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.022, size = 136, normalized size = 5.7 \begin{align*} -{\frac{{b}^{8}}{n{x}^{n}}}-4\,{\frac{{b}^{7}a}{n \left ({x}^{n} \right ) ^{2}}}-{\frac{28\,{a}^{2}{b}^{6}}{3\,n \left ({x}^{n} \right ) ^{3}}}-14\,{\frac{{a}^{3}{b}^{5}}{n \left ({x}^{n} \right ) ^{4}}}-14\,{\frac{{a}^{4}{b}^{4}}{n \left ({x}^{n} \right ) ^{5}}}-{\frac{28\,{a}^{5}{b}^{3}}{3\,n \left ({x}^{n} \right ) ^{6}}}-4\,{\frac{{a}^{6}{b}^{2}}{n \left ({x}^{n} \right ) ^{7}}}-{\frac{b{a}^{7}}{n \left ({x}^{n} \right ) ^{8}}}-{\frac{{a}^{8}}{9\,n \left ({x}^{n} \right ) ^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.03167, size = 243, normalized size = 10.12 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.24986, size = 150, normalized size = 6.25 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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