Optimal. Leaf size=30 \[ \frac {a^2 x^7}{7}+\frac {2}{5} a b x^5+\frac {b^2 x^3}{3} \]
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Rubi [A] time = 0.01, antiderivative size = 30, 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, 270} \[ \frac {a^2 x^7}{7}+\frac {2}{5} a b x^5+\frac {b^2 x^3}{3} \]
Antiderivative was successfully verified.
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Rule 263
Rule 270
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x^2}\right )^2 x^6 \, dx &=\int x^2 \left (b+a x^2\right )^2 \, dx\\ &=\int \left (b^2 x^2+2 a b x^4+a^2 x^6\right ) \, dx\\ &=\frac {b^2 x^3}{3}+\frac {2}{5} a b x^5+\frac {a^2 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \[ \frac {a^2 x^7}{7}+\frac {2}{5} a b x^5+\frac {b^2 x^3}{3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 24, normalized size = 0.80 \[ \frac {1}{7} \, a^{2} x^{7} + \frac {2}{5} \, a b x^{5} + \frac {1}{3} \, b^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 24, normalized size = 0.80 \[ \frac {1}{7} \, a^{2} x^{7} + \frac {2}{5} \, a b x^{5} + \frac {1}{3} \, b^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.83 \[ \frac {1}{7} a^{2} x^{7}+\frac {2}{5} a b \,x^{5}+\frac {1}{3} b^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.80, size = 24, normalized size = 0.80 \[ \frac {1}{7} \, a^{2} x^{7} + \frac {2}{5} \, a b x^{5} + \frac {1}{3} \, b^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 24, normalized size = 0.80 \[ \frac {a^2\,x^7}{7}+\frac {2\,a\,b\,x^5}{5}+\frac {b^2\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 26, normalized size = 0.87 \[ \frac {a^{2} x^{7}}{7} + \frac {2 a b x^{5}}{5} + \frac {b^{2} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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