Optimal. Leaf size=20 \[ -\frac{a^2}{x}+2 a b \log (x)+b^2 x \]
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Rubi [A] time = 0.0081317, antiderivative size = 20, 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} \[ -\frac{a^2}{x}+2 a b \log (x)+b^2 x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^2}{x^2} \, dx &=\int \left (b^2+\frac{a^2}{x^2}+\frac{2 a b}{x}\right ) \, dx\\ &=-\frac{a^2}{x}+b^2 x+2 a b \log (x)\\ \end{align*}
Mathematica [A] time = 0.0010358, size = 20, normalized size = 1. \[ -\frac{a^2}{x}+2 a b \log (x)+b^2 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 21, normalized size = 1.1 \begin{align*} -{\frac{{a}^{2}}{x}}+{b}^{2}x+2\,ab\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02448, size = 27, normalized size = 1.35 \begin{align*} b^{2} x + 2 \, a b \log \left (x\right ) - \frac{a^{2}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59555, size = 49, normalized size = 2.45 \begin{align*} \frac{b^{2} x^{2} + 2 \, a b x \log \left (x\right ) - a^{2}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.30444, size = 17, normalized size = 0.85 \begin{align*} - \frac{a^{2}}{x} + 2 a b \log{\left (x \right )} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15834, size = 28, normalized size = 1.4 \begin{align*} b^{2} x + 2 \, a b \log \left ({\left | x \right |}\right ) - \frac{a^{2}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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