Optimal. Leaf size=35 \[ \frac {a^3 x^7}{7}+\frac {3}{5} a^2 b x^5+a b^2 x^3+b^3 x \]
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Rubi [A] time = 0.01, antiderivative size = 35, 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, 194} \[ \frac {3}{5} a^2 b x^5+\frac {a^3 x^7}{7}+a b^2 x^3+b^3 x \]
Antiderivative was successfully verified.
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Rule 194
Rule 263
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x^2}\right )^3 x^6 \, dx &=\int \left (b+a x^2\right )^3 \, dx\\ &=\int \left (b^3+3 a b^2 x^2+3 a^2 b x^4+a^3 x^6\right ) \, dx\\ &=b^3 x+a b^2 x^3+\frac {3}{5} a^2 b x^5+\frac {a^3 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 35, normalized size = 1.00 \[ \frac {a^3 x^7}{7}+\frac {3}{5} a^2 b x^5+a b^2 x^3+b^3 x \]
Antiderivative was successfully verified.
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fricas [A] time = 1.31, size = 31, normalized size = 0.89 \[ \frac {1}{7} \, a^{3} x^{7} + \frac {3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 31, normalized size = 0.89 \[ \frac {1}{7} \, a^{3} x^{7} + \frac {3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 32, normalized size = 0.91 \[ \frac {1}{7} a^{3} x^{7}+\frac {3}{5} a^{2} b \,x^{5}+a \,b^{2} x^{3}+b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 31, normalized size = 0.89 \[ \frac {1}{7} \, a^{3} x^{7} + \frac {3}{5} \, a^{2} b x^{5} + a b^{2} x^{3} + b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 31, normalized size = 0.89 \[ \frac {a^3\,x^7}{7}+\frac {3\,a^2\,b\,x^5}{5}+a\,b^2\,x^3+b^3\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 32, normalized size = 0.91 \[ \frac {a^{3} x^{7}}{7} + \frac {3 a^{2} b x^{5}}{5} + a b^{2} x^{3} + b^{3} x \]
Verification of antiderivative is not currently implemented for this CAS.
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