Optimal. Leaf size=17 \[ \frac {a x^3}{3}+\frac {b x^2}{2} \]
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Rubi [A] time = 0.01, antiderivative size = 17, 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} \[ \frac {a x^3}{3}+\frac {b x^2}{2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x}\right ) x^2 \, dx &=\int \left (b x+a x^2\right ) \, dx\\ &=\frac {b x^2}{2}+\frac {a x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {a x^3}{3}+\frac {b x^2}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 13, normalized size = 0.76 \[ \frac {1}{3} \, a x^{3} + \frac {1}{2} \, b x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.76 \[ \frac {1}{3} \, a x^{3} + \frac {1}{2} \, b x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \[ \frac {1}{3} a \,x^{3}+\frac {1}{2} b \,x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 13, normalized size = 0.76 \[ \frac {1}{3} \, a x^{3} + \frac {1}{2} \, b x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.76 \[ \frac {x^2\,\left (3\,b+2\,a\,x\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 12, normalized size = 0.71 \[ \frac {a x^{3}}{3} + \frac {b x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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