Optimal. Leaf size=16 \[ \frac {\left (a x^2+b\right )^3}{6 a} \]
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Rubi [A] time = 0.00, antiderivative size = 16, 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, 261} \[ \frac {\left (a x^2+b\right )^3}{6 a} \]
Antiderivative was successfully verified.
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Rule 261
Rule 263
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x^2}\right )^2 x^5 \, dx &=\int x \left (b+a x^2\right )^2 \, dx\\ &=\frac {\left (b+a x^2\right )^3}{6 a}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {\left (a x^2+b\right )^3}{6 a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 24, normalized size = 1.50 \[ \frac {1}{6} \, a^{2} x^{6} + \frac {1}{2} \, a b x^{4} + \frac {1}{2} \, b^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 24, normalized size = 1.50 \[ \frac {1}{6} \, a^{2} x^{6} + \frac {1}{2} \, a b x^{4} + \frac {1}{2} \, b^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 1.56 \[ \frac {1}{6} a^{2} x^{6}+\frac {1}{2} a b \,x^{4}+\frac {1}{2} b^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 24, normalized size = 1.50 \[ \frac {1}{6} \, a^{2} x^{6} + \frac {1}{2} \, a b x^{4} + \frac {1}{2} \, b^{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 1.50 \[ \frac {a^2\,x^6}{6}+\frac {a\,b\,x^4}{2}+\frac {b^2\,x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 24, normalized size = 1.50 \[ \frac {a^{2} x^{6}}{6} + \frac {a b x^{4}}{2} + \frac {b^{2} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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