Optimal. Leaf size=12 \[ \frac {a x^3}{3}+b x \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ \frac {a x^3}{3}+b x \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x^2}\right ) x^2 \, dx &=\int \left (b+a x^2\right ) \, dx\\ &=b x+\frac {a x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ \frac {a x^3}{3}+b x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 10, normalized size = 0.83 \[ \frac {1}{3} \, a x^{3} + b x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 10, normalized size = 0.83 \[ \frac {1}{3} \, a x^{3} + b x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.92 \[ \frac {1}{3} a \,x^{3}+b x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.04, size = 10, normalized size = 0.83 \[ \frac {1}{3} \, a x^{3} + b x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 10, normalized size = 0.83 \[ \frac {a\,x^3}{3}+b\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 8, normalized size = 0.67 \[ \frac {a x^{3}}{3} + b x \]
Verification of antiderivative is not currently implemented for this CAS.
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