Optimal. Leaf size=22 \[ a^2 \log (x)+2 a b x+\frac{b^2 x^2}{2} \]
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Rubi [A] time = 0.006339, antiderivative size = 22, 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} \[ a^2 \log (x)+2 a b x+\frac{b^2 x^2}{2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^2}{x} \, dx &=\int \left (2 a b+\frac{a^2}{x}+b^2 x\right ) \, dx\\ &=2 a b x+\frac{b^2 x^2}{2}+a^2 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0007976, size = 22, normalized size = 1. \[ a^2 \log (x)+2 a b x+\frac{b^2 x^2}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 21, normalized size = 1. \begin{align*} 2\,abx+{\frac{{b}^{2}{x}^{2}}{2}}+{a}^{2}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07302, size = 27, normalized size = 1.23 \begin{align*} \frac{1}{2} \, b^{2} x^{2} + 2 \, a b x + a^{2} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48218, size = 49, normalized size = 2.23 \begin{align*} \frac{1}{2} \, b^{2} x^{2} + 2 \, a b x + a^{2} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.328913, size = 20, normalized size = 0.91 \begin{align*} a^{2} \log{\left (x \right )} + 2 a b x + \frac{b^{2} x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13502, size = 28, normalized size = 1.27 \begin{align*} \frac{1}{2} \, b^{2} x^{2} + 2 \, a b x + a^{2} \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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