Optimal. Leaf size=22 \[ \frac {a^2 x^2}{2}+2 a b x+b^2 \log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {263, 43} \[ \frac {a^2 x^2}{2}+2 a b x+b^2 \log (x) \]
Antiderivative was successfully verified.
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Rule 43
Rule 263
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x}\right )^2 x \, dx &=\int \frac {(b+a x)^2}{x} \, dx\\ &=\int \left (2 a b+\frac {b^2}{x}+a^2 x\right ) \, dx\\ &=2 a b x+\frac {a^2 x^2}{2}+b^2 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ \frac {a^2 x^2}{2}+2 a b x+b^2 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 20, normalized size = 0.91 \[ \frac {1}{2} \, a^{2} x^{2} + 2 \, a b x + b^{2} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 21, normalized size = 0.95 \[ \frac {1}{2} \, a^{2} x^{2} + 2 \, a b x + b^{2} \log \left ({\left | x \right |}\right ) \]
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 \[ \frac {a^{2} x^{2}}{2}+2 a b x +b^{2} \ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.05, size = 20, normalized size = 0.91 \[ \frac {1}{2} \, a^{2} x^{2} + 2 \, a b x + b^{2} \log \relax (x) \]
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 \[ b^2\,\ln \relax (x)+\frac {a^2\,x^2}{2}+2\,a\,b\,x \]
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 \[ \frac {a^{2} x^{2}}{2} + 2 a b x + b^{2} \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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