Optimal. Leaf size=43 \[ \frac {a^3 x^6}{6}+\frac {3}{5} a^2 b x^5+\frac {3}{4} a b^2 x^4+\frac {b^3 x^3}{3} \]
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Rubi [A] time = 0.02, antiderivative size = 43, 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} \[ \frac {3}{5} a^2 b x^5+\frac {a^3 x^6}{6}+\frac {3}{4} a b^2 x^4+\frac {b^3 x^3}{3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 263
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x}\right )^3 x^5 \, dx &=\int x^2 (b+a x)^3 \, dx\\ &=\int \left (b^3 x^2+3 a b^2 x^3+3 a^2 b x^4+a^3 x^5\right ) \, dx\\ &=\frac {b^3 x^3}{3}+\frac {3}{4} a b^2 x^4+\frac {3}{5} a^2 b x^5+\frac {a^3 x^6}{6}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \[ \frac {a^3 x^6}{6}+\frac {3}{5} a^2 b x^5+\frac {3}{4} a b^2 x^4+\frac {b^3 x^3}{3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 35, normalized size = 0.81 \[ \frac {1}{6} \, a^{3} x^{6} + \frac {3}{5} \, a^{2} b x^{5} + \frac {3}{4} \, a b^{2} x^{4} + \frac {1}{3} \, b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 35, normalized size = 0.81 \[ \frac {1}{6} \, a^{3} x^{6} + \frac {3}{5} \, a^{2} b x^{5} + \frac {3}{4} \, a b^{2} x^{4} + \frac {1}{3} \, b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.84 \[ \frac {1}{6} a^{3} x^{6}+\frac {3}{5} a^{2} b \,x^{5}+\frac {3}{4} a \,b^{2} x^{4}+\frac {1}{3} b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.11, size = 35, normalized size = 0.81 \[ \frac {1}{6} \, a^{3} x^{6} + \frac {3}{5} \, a^{2} b x^{5} + \frac {3}{4} \, a b^{2} x^{4} + \frac {1}{3} \, b^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.81 \[ \frac {a^3\,x^6}{6}+\frac {3\,a^2\,b\,x^5}{5}+\frac {3\,a\,b^2\,x^4}{4}+\frac {b^3\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 39, normalized size = 0.91 \[ \frac {a^{3} x^{6}}{6} + \frac {3 a^{2} b x^{5}}{5} + \frac {3 a b^{2} x^{4}}{4} + \frac {b^{3} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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