Optimal. Leaf size=35 \[ 3 a^2 b x+a^3 \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3} \]
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Rubi [A] time = 0.0105865, antiderivative size = 35, 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} \[ 3 a^2 b x+a^3 \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^3}{x} \, dx &=\int \left (3 a^2 b+\frac{a^3}{x}+3 a b^2 x+b^3 x^2\right ) \, dx\\ &=3 a^2 b x+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3}+a^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0050428, size = 35, normalized size = 1. \[ 3 a^2 b x+a^3 \log (x)+\frac{3}{2} a b^2 x^2+\frac{b^3 x^3}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 32, normalized size = 0.9 \begin{align*} 3\,{a}^{2}bx+{\frac{3\,a{b}^{2}{x}^{2}}{2}}+{\frac{{b}^{3}{x}^{3}}{3}}+{a}^{3}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04152, size = 42, normalized size = 1.2 \begin{align*} \frac{1}{3} \, b^{3} x^{3} + \frac{3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50323, size = 73, normalized size = 2.09 \begin{align*} \frac{1}{3} \, b^{3} x^{3} + \frac{3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.310695, size = 34, normalized size = 0.97 \begin{align*} a^{3} \log{\left (x \right )} + 3 a^{2} b x + \frac{3 a b^{2} x^{2}}{2} + \frac{b^{3} x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16073, size = 43, normalized size = 1.23 \begin{align*} \frac{1}{3} \, b^{3} x^{3} + \frac{3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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