Optimal. Leaf size=17 \[ -\frac{(a+b x)^3}{3 a x^3} \]
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Rubi [A] time = 0.0015496, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {37} \[ -\frac{(a+b x)^3}{3 a x^3} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{(a+b x)^2}{x^4} \, dx &=-\frac{(a+b x)^3}{3 a x^3}\\ \end{align*}
Mathematica [A] time = 0.0073309, size = 26, normalized size = 1.53 \[ -\frac{a^2}{3 x^3}-\frac{a b}{x^2}-\frac{b^2}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 25, normalized size = 1.5 \begin{align*} -{\frac{{a}^{2}}{3\,{x}^{3}}}-{\frac{ab}{{x}^{2}}}-{\frac{{b}^{2}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00007, size = 30, normalized size = 1.76 \begin{align*} -\frac{3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46217, size = 51, normalized size = 3. \begin{align*} -\frac{3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.369987, size = 24, normalized size = 1.41 \begin{align*} - \frac{a^{2} + 3 a b x + 3 b^{2} x^{2}}{3 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12523, size = 30, normalized size = 1.76 \begin{align*} -\frac{3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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