Optimal. Leaf size=14 \[ \frac {(a x+b)^9}{9 a} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, 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 32
Rule 263
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*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {(a x+b)^9}{9 a} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.86, size = 86, normalized size = 6.14 \[ \frac {1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac {28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac {28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 86, normalized size = 6.14 \[ \frac {1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac {28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac {28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.93 \[ \frac {\left (a x +b \right )^{9}}{9 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.97, size = 86, normalized size = 6.14 \[ \frac {1}{9} \, a^{8} x^{9} + a^{7} b x^{8} + 4 \, a^{6} b^{2} x^{7} + \frac {28}{3} \, a^{5} b^{3} x^{6} + 14 \, a^{4} b^{4} x^{5} + 14 \, a^{3} b^{5} x^{4} + \frac {28}{3} \, a^{2} b^{6} x^{3} + 4 \, a b^{7} x^{2} + b^{8} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 86, normalized size = 6.14 \[ \frac {a^8\,x^9}{9}+a^7\,b\,x^8+4\,a^6\,b^2\,x^7+\frac {28\,a^5\,b^3\,x^6}{3}+14\,a^4\,b^4\,x^5+14\,a^3\,b^5\,x^4+\frac {28\,a^2\,b^6\,x^3}{3}+4\,a\,b^7\,x^2+b^8\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 94, normalized size = 6.71 \[ \frac {a^{8} x^{9}}{9} + a^{7} b x^{8} + 4 a^{6} b^{2} x^{7} + \frac {28 a^{5} b^{3} x^{6}}{3} + 14 a^{4} b^{4} x^{5} + 14 a^{3} b^{5} x^{4} + \frac {28 a^{2} b^{6} x^{3}}{3} + 4 a b^{7} x^{2} + b^{8} x \]
Verification of antiderivative is not currently implemented for this CAS.
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