Optimal. Leaf size=33 \[ -\frac {a^3}{2 x^2}-\frac {3 a^2 b}{x}+3 a b^2 \log (x)+b^3 x \]
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Rubi [A] time = 0.01, antiderivative size = 33, 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} \[ -\frac {3 a^2 b}{x}-\frac {a^3}{2 x^2}+3 a b^2 \log (x)+b^3 x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{x^3} \, dx &=\int \left (b^3+\frac {a^3}{x^3}+\frac {3 a^2 b}{x^2}+\frac {3 a b^2}{x}\right ) \, dx\\ &=-\frac {a^3}{2 x^2}-\frac {3 a^2 b}{x}+b^3 x+3 a b^2 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 1.00 \[ -\frac {a^3}{2 x^2}-\frac {3 a^2 b}{x}+3 a b^2 \log (x)+b^3 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 37, normalized size = 1.12 \[ \frac {2 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} \log \relax (x) - 6 \, a^{2} b x - a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 31, normalized size = 0.94 \[ b^{3} x + 3 \, a b^{2} \log \left ({\left | x \right |}\right ) - \frac {6 \, a^{2} b x + a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 32, normalized size = 0.97 \[ 3 a \,b^{2} \ln \relax (x )+b^{3} x -\frac {3 a^{2} b}{x}-\frac {a^{3}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 30, normalized size = 0.91 \[ b^{3} x + 3 \, a b^{2} \log \relax (x) - \frac {6 \, a^{2} b x + a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 32, normalized size = 0.97 \[ b^3\,x-\frac {\frac {a^3}{2}+3\,b\,x\,a^2}{x^2}+3\,a\,b^2\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 32, normalized size = 0.97 \[ 3 a b^{2} \log {\relax (x )} + b^{3} x + \frac {- a^{3} - 6 a^{2} b x}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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