Optimal. Leaf size=14 \[ \frac{(a x+b)^3}{3 a} \]
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Rubi [A] time = 0.00388, antiderivative size = 14, normalized size of antiderivative = 1., 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, 32} \[ \frac{(a x+b)^3}{3 a} \]
Antiderivative was successfully verified.
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Rule 263
Rule 32
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x}\right )^2 x^2 \, dx &=\int (b+a x)^2 \, dx\\ &=\frac{(b+a x)^3}{3 a}\\ \end{align*}
Mathematica [A] time = 0.0012913, size = 14, normalized size = 1. \[ \frac{(a x+b)^3}{3 a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \begin{align*}{\frac{ \left ( ax+b \right ) ^{3}}{3\,a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.950026, size = 27, normalized size = 1.93 \begin{align*} \frac{1}{3} \, a^{2} x^{3} + a b x^{2} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38927, size = 42, normalized size = 3. \begin{align*} \frac{1}{3} \, a^{2} x^{3} + a b x^{2} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.057442, size = 19, normalized size = 1.36 \begin{align*} \frac{a^{2} x^{3}}{3} + a b x^{2} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17633, size = 27, normalized size = 1.93 \begin{align*} \frac{1}{3} \, a^{2} x^{3} + a b x^{2} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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