Optimal. Leaf size=20 \[ a^2 x+2 a b \log (x)-\frac {b^2}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {193, 43} \[ a^2 x+2 a b \log (x)-\frac {b^2}{x} \]
Antiderivative was successfully verified.
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Rule 43
Rule 193
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x}\right )^2 \, dx &=\int \frac {(b+a x)^2}{x^2} \, dx\\ &=\int \left (a^2+\frac {b^2}{x^2}+\frac {2 a b}{x}\right ) \, dx\\ &=-\frac {b^2}{x}+a^2 x+2 a b \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \[ a^2 x+2 a b \log (x)-\frac {b^2}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 24, normalized size = 1.20 \[ \frac {a^{2} x^{2} + 2 \, a b x \log \relax (x) - b^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 21, normalized size = 1.05 \[ a^{2} x + 2 \, a b \log \left ({\left | x \right |}\right ) - \frac {b^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 21, normalized size = 1.05 \[ a^{2} x +2 a b \ln \relax (x )-\frac {b^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.05, size = 20, normalized size = 1.00 \[ a^{2} x + 2 \, a b \log \relax (x) - \frac {b^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 20, normalized size = 1.00 \[ a^2\,x-\frac {b^2}{x}+2\,a\,b\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 17, normalized size = 0.85 \[ a^{2} x + 2 a b \log {\relax (x )} - \frac {b^{2}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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