Optimal. Leaf size=34 \[ -\frac {a^3}{x}+3 a^2 b \log (x)+3 a b^2 x+\frac {b^3 x^2}{2} \]
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Rubi [A] time = 0.01, antiderivative size = 34, 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} \[ 3 a^2 b \log (x)-\frac {a^3}{x}+3 a b^2 x+\frac {b^3 x^2}{2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{x^2} \, dx &=\int \left (3 a b^2+\frac {a^3}{x^2}+\frac {3 a^2 b}{x}+b^3 x\right ) \, dx\\ &=-\frac {a^3}{x}+3 a b^2 x+\frac {b^3 x^2}{2}+3 a^2 b \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 34, normalized size = 1.00 \[ -\frac {a^3}{x}+3 a^2 b \log (x)+3 a b^2 x+\frac {b^3 x^2}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 36, normalized size = 1.06 \[ \frac {b^{3} x^{3} + 6 \, a b^{2} x^{2} + 6 \, a^{2} b x \log \relax (x) - 2 \, a^{3}}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.36, size = 33, normalized size = 0.97 \[ \frac {1}{2} \, b^{3} x^{2} + 3 \, a b^{2} x + 3 \, a^{2} b \log \left ({\left | x \right |}\right ) - \frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 33, normalized size = 0.97 \[ \frac {b^{3} x^{2}}{2}+3 a^{2} b \ln \relax (x )+3 a \,b^{2} x -\frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 32, normalized size = 0.94 \[ \frac {1}{2} \, b^{3} x^{2} + 3 \, a b^{2} x + 3 \, a^{2} b \log \relax (x) - \frac {a^{3}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 32, normalized size = 0.94 \[ \frac {b^3\,x^2}{2}-\frac {a^3}{x}+3\,a^2\,b\,\ln \relax (x)+3\,a\,b^2\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 31, normalized size = 0.91 \[ - \frac {a^{3}}{x} + 3 a^{2} b \log {\relax (x )} + 3 a b^{2} x + \frac {b^{3} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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