Optimal. Leaf size=34 \[ 3 a^2 b \log (x)-\frac{a^3}{x}+3 a b^2 x+\frac{b^3 x^2}{2} \]
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Rubi [A] time = 0.0132317, antiderivative size = 34, normalized size of antiderivative = 1., 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 = {43} \[ 3 a^2 b \log (x)-\frac{a^3}{x}+3 a b^2 x+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^3}{x^2} \, dx &=\int \left (3 a b^2+\frac{a^3}{x^2}+\frac{3 a^2 b}{x}+b^3 x\right ) \, dx\\ &=-\frac{a^3}{x}+3 a b^2 x+\frac{b^3 x^2}{2}+3 a^2 b \log (x)\\ \end{align*}
Mathematica [A] time = 0.0064276, size = 34, normalized size = 1. \[ 3 a^2 b \log (x)-\frac{a^3}{x}+3 a b^2 x+\frac{b^3 x^2}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 33, normalized size = 1. \begin{align*} -{\frac{{a}^{3}}{x}}+3\,a{b}^{2}x+{\frac{{b}^{3}{x}^{2}}{2}}+3\,{a}^{2}b\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07062, size = 43, normalized size = 1.26 \begin{align*} \frac{1}{2} \, b^{3} x^{2} + 3 \, a b^{2} x + 3 \, a^{2} b \log \left (x\right ) - \frac{a^{3}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50798, size = 78, normalized size = 2.29 \begin{align*} \frac{b^{3} x^{3} + 6 \, a b^{2} x^{2} + 6 \, a^{2} b x \log \left (x\right ) - 2 \, a^{3}}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.316417, size = 31, normalized size = 0.91 \begin{align*} - \frac{a^{3}}{x} + 3 a^{2} b \log{\left (x \right )} + 3 a b^{2} x + \frac{b^{3} x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1732, size = 45, normalized size = 1.32 \begin{align*} \frac{1}{2} \, b^{3} x^{2} + 3 \, a b^{2} x + 3 \, a^{2} b \log \left ({\left | x \right |}\right ) - \frac{a^{3}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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