Optimal. Leaf size=37 \[ -\frac{3 a^2 b}{2 x^2}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{x}+b^3 \log (x) \]
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Rubi [A] time = 0.0122868, antiderivative size = 37, normalized size of antiderivative = 1., 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} \[ -\frac{3 a^2 b}{2 x^2}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{x}+b^3 \log (x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^3}{x^4} \, dx &=\int \left (\frac{a^3}{x^4}+\frac{3 a^2 b}{x^3}+\frac{3 a b^2}{x^2}+\frac{b^3}{x}\right ) \, dx\\ &=-\frac{a^3}{3 x^3}-\frac{3 a^2 b}{2 x^2}-\frac{3 a b^2}{x}+b^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0037367, size = 37, normalized size = 1. \[ -\frac{3 a^2 b}{2 x^2}-\frac{a^3}{3 x^3}-\frac{3 a b^2}{x}+b^3 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 34, normalized size = 0.9 \begin{align*} -{\frac{{a}^{3}}{3\,{x}^{3}}}-{\frac{3\,{a}^{2}b}{2\,{x}^{2}}}-3\,{\frac{{b}^{2}a}{x}}+{b}^{3}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04267, size = 46, normalized size = 1.24 \begin{align*} b^{3} \log \left (x\right ) - \frac{18 \, a b^{2} x^{2} + 9 \, a^{2} b x + 2 \, a^{3}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.58624, size = 85, normalized size = 2.3 \begin{align*} \frac{6 \, b^{3} x^{3} \log \left (x\right ) - 18 \, a b^{2} x^{2} - 9 \, a^{2} b x - 2 \, a^{3}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.56435, size = 34, normalized size = 0.92 \begin{align*} b^{3} \log{\left (x \right )} - \frac{2 a^{3} + 9 a^{2} b x + 18 a b^{2} x^{2}}{6 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19726, size = 47, normalized size = 1.27 \begin{align*} b^{3} \log \left ({\left | x \right |}\right ) - \frac{18 \, a b^{2} x^{2} + 9 \, a^{2} b x + 2 \, a^{3}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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