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 = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, 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} \begin {gather*} a^2 \log (x)+2 a b x+\frac {b^2 x^2}{2} \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} a^2 \log (x)+2 a b x+\frac {b^2 x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^2}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.84, size = 20, normalized size = 0.91 \begin {gather*} \frac {1}{2} \, b^{2} x^{2} + 2 \, a b x + a^{2} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.35, size = 21, normalized size = 0.95 \begin {gather*} \frac {1}{2} \, b^{2} x^{2} + 2 \, a b x + a^{2} \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 0.95 \begin {gather*} \frac {b^{2} x^{2}}{2}+a^{2} \ln \relax (x )+2 a b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.11, size = 20, normalized size = 0.91 \begin {gather*} \frac {1}{2} \, b^{2} x^{2} + 2 \, a b x + a^{2} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 20, normalized size = 0.91 \begin {gather*} a^2\,\ln \relax (x)+\frac {b^2\,x^2}{2}+2\,a\,b\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 20, normalized size = 0.91 \begin {gather*} a^{2} \log {\relax (x )} + 2 a b x + \frac {b^{2} x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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