Optimal. Leaf size=30 \[ -\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2} \]
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Rubi [A] time = 0.0078972, antiderivative size = 30, 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} \[ -\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(a+b x)^2}{x^5} \, dx &=\int \left (\frac{a^2}{x^5}+\frac{2 a b}{x^4}+\frac{b^2}{x^3}\right ) \, dx\\ &=-\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0052963, size = 30, normalized size = 1. \[ -\frac{a^2}{4 x^4}-\frac{2 a b}{3 x^3}-\frac{b^2}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{a}^{2}}{4\,{x}^{4}}}-{\frac{2\,ab}{3\,{x}^{3}}}-{\frac{{b}^{2}}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02448, size = 32, normalized size = 1.07 \begin{align*} -\frac{6 \, b^{2} x^{2} + 8 \, a b x + 3 \, a^{2}}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50164, size = 55, normalized size = 1.83 \begin{align*} -\frac{6 \, b^{2} x^{2} + 8 \, a b x + 3 \, a^{2}}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.355127, size = 26, normalized size = 0.87 \begin{align*} - \frac{3 a^{2} + 8 a b x + 6 b^{2} x^{2}}{12 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16497, size = 32, normalized size = 1.07 \begin{align*} -\frac{6 \, b^{2} x^{2} + 8 \, a b x + 3 \, a^{2}}{12 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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