Optimal. Leaf size=36 \[ \log (x) (a B+A b)-\frac {a A}{x}+x (A c+b B)+\frac {1}{2} B c x^2 \]
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Rubi [A] time = 0.03, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {765} \[ \log (x) (a B+A b)-\frac {a A}{x}+x (A c+b B)+\frac {1}{2} B c x^2 \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a+b x+c x^2\right )}{x^2} \, dx &=\int \left (b B \left (1+\frac {A c}{b B}\right )+\frac {a A}{x^2}+\frac {A b+a B}{x}+B c x\right ) \, dx\\ &=-\frac {a A}{x}+(b B+A c) x+\frac {1}{2} B c x^2+(A b+a B) \log (x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 36, normalized size = 1.00 \[ \log (x) (a B+A b)-\frac {a A}{x}+x (A c+b B)+\frac {1}{2} B c x^2 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 40, normalized size = 1.11 \[ \frac {B c x^{3} + 2 \, {\left (B b + A c\right )} x^{2} + 2 \, {\left (B a + A b\right )} x \log \relax (x) - 2 \, A a}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 34, normalized size = 0.94 \[ \frac {1}{2} \, B c x^{2} + B b x + A c x + {\left (B a + A b\right )} \log \left ({\left | x \right |}\right ) - \frac {A a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 34, normalized size = 0.94 \[ \frac {B c \,x^{2}}{2}+A b \ln \relax (x )+A c x +B a \ln \relax (x )+B b x -\frac {A a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 34, normalized size = 0.94 \[ \frac {1}{2} \, B c x^{2} + {\left (B b + A c\right )} x + {\left (B a + A b\right )} \log \relax (x) - \frac {A a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 34, normalized size = 0.94 \[ x\,\left (A\,c+B\,b\right )+\ln \relax (x)\,\left (A\,b+B\,a\right )-\frac {A\,a}{x}+\frac {B\,c\,x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 31, normalized size = 0.86 \[ - \frac {A a}{x} + \frac {B c x^{2}}{2} + x \left (A c + B b\right ) + \left (A b + B a\right ) \log {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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