Optimal. Leaf size=17 \[ -\frac{a}{3 x^3}-\frac{b}{2 x^2} \]
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Rubi [A] time = 0.0047191, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ -\frac{a}{3 x^3}-\frac{b}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{x^4} \, dx &=\int \left (\frac{a}{x^4}+\frac{b}{x^3}\right ) \, dx\\ &=-\frac{a}{3 x^3}-\frac{b}{2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0020062, size = 17, normalized size = 1. \[ -\frac{a}{3 x^3}-\frac{b}{2 x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 14, normalized size = 0.8 \begin{align*} -{\frac{a}{3\,{x}^{3}}}-{\frac{b}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0356, size = 18, normalized size = 1.06 \begin{align*} -\frac{3 \, b x + 2 \, a}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.62695, size = 32, normalized size = 1.88 \begin{align*} -\frac{3 \, b x + 2 \, a}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.424286, size = 14, normalized size = 0.82 \begin{align*} - \frac{2 a + 3 b x}{6 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17997, size = 18, normalized size = 1.06 \begin{align*} -\frac{3 \, b x + 2 \, a}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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