Optimal. Leaf size=14 \[ \frac{(a x+b)^9}{9 a} \]
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Rubi [A] time = 0.0038971, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 32} \[ \frac{(a x+b)^9}{9 a} \]
Antiderivative was successfully verified.
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Rule 263
Rule 32
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x}\right )^8 x^8 \, dx &=\int (b+a x)^8 \, dx\\ &=\frac{(b+a x)^9}{9 a}\\ \end{align*}
Mathematica [A] time = 0.0010183, size = 14, normalized size = 1. \[ \frac{(a x+b)^9}{9 a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( ax+b \right ) ^{9}}{9\,a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.96903, size = 116, normalized size = 8.29 \begin{align*} \frac{1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac{28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.38618, size = 182, normalized size = 13. \begin{align*} \frac{1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac{28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.077618, size = 94, normalized size = 6.71 \begin{align*} \frac{a^{8} x^{9}}{9} + a^{7} b x^{8} + 4 a^{6} b^{2} x^{7} + \frac{28 a^{5} b^{3} x^{6}}{3} + 14 a^{4} b^{4} x^{5} + 14 a^{3} b^{5} x^{4} + \frac{28 a^{2} b^{6} x^{3}}{3} + 4 a b^{7} x^{2} + b^{8} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.53018, size = 116, normalized size = 8.29 \begin{align*} \frac{1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac{28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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