Optimal. Leaf size=47 \[ \frac {b^2 (a x+b)^9}{9 a^3}+\frac {(a x+b)^{11}}{11 a^3}-\frac {b (a x+b)^{10}}{5 a^3} \]
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Rubi [A] time = 0.03, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {263, 43} \[ \frac {b^2 (a x+b)^9}{9 a^3}+\frac {(a x+b)^{11}}{11 a^3}-\frac {b (a x+b)^{10}}{5 a^3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 263
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x}\right )^8 x^{10} \, dx &=\int x^2 (b+a x)^8 \, dx\\ &=\int \left (\frac {b^2 (b+a x)^8}{a^2}-\frac {2 b (b+a x)^9}{a^2}+\frac {(b+a x)^{10}}{a^2}\right ) \, dx\\ &=\frac {b^2 (b+a x)^9}{9 a^3}-\frac {b (b+a x)^{10}}{5 a^3}+\frac {(b+a x)^{11}}{11 a^3}\\ \end {align*}
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Mathematica [B] time = 0.00, size = 102, normalized size = 2.17 \[ \frac {a^8 x^{11}}{11}+\frac {4}{5} a^7 b x^{10}+\frac {28}{9} a^6 b^2 x^9+7 a^5 b^3 x^8+10 a^4 b^4 x^7+\frac {28}{3} a^3 b^5 x^6+\frac {28}{5} a^2 b^6 x^5+2 a b^7 x^4+\frac {b^8 x^3}{3} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.90, size = 90, normalized size = 1.91 \[ \frac {1}{11} \, a^{8} x^{11} + \frac {4}{5} \, a^{7} b x^{10} + \frac {28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac {28}{3} \, a^{3} b^{5} x^{6} + \frac {28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac {1}{3} \, b^{8} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 90, normalized size = 1.91 \[ \frac {1}{11} \, a^{8} x^{11} + \frac {4}{5} \, a^{7} b x^{10} + \frac {28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac {28}{3} \, a^{3} b^{5} x^{6} + \frac {28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac {1}{3} \, b^{8} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 91, normalized size = 1.94 \[ \frac {1}{11} a^{8} x^{11}+\frac {4}{5} a^{7} b \,x^{10}+\frac {28}{9} a^{6} b^{2} x^{9}+7 a^{5} b^{3} x^{8}+10 a^{4} b^{4} x^{7}+\frac {28}{3} a^{3} b^{5} x^{6}+\frac {28}{5} a^{2} b^{6} x^{5}+2 a \,b^{7} x^{4}+\frac {1}{3} b^{8} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.96, size = 90, normalized size = 1.91 \[ \frac {1}{11} \, a^{8} x^{11} + \frac {4}{5} \, a^{7} b x^{10} + \frac {28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac {28}{3} \, a^{3} b^{5} x^{6} + \frac {28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac {1}{3} \, b^{8} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.06, size = 90, normalized size = 1.91 \[ \frac {a^8\,x^{11}}{11}+\frac {4\,a^7\,b\,x^{10}}{5}+\frac {28\,a^6\,b^2\,x^9}{9}+7\,a^5\,b^3\,x^8+10\,a^4\,b^4\,x^7+\frac {28\,a^3\,b^5\,x^6}{3}+\frac {28\,a^2\,b^6\,x^5}{5}+2\,a\,b^7\,x^4+\frac {b^8\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.09, size = 102, normalized size = 2.17 \[ \frac {a^{8} x^{11}}{11} + \frac {4 a^{7} b x^{10}}{5} + \frac {28 a^{6} b^{2} x^{9}}{9} + 7 a^{5} b^{3} x^{8} + 10 a^{4} b^{4} x^{7} + \frac {28 a^{3} b^{5} x^{6}}{3} + \frac {28 a^{2} b^{6} x^{5}}{5} + 2 a b^{7} x^{4} + \frac {b^{8} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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