Optimal. Leaf size=12 \[ b x-\frac{a}{3 x^3} \]
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Rubi [A] time = 0.0042222, antiderivative size = 12, 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 = {14} \[ b x-\frac{a}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+b x^4}{x^4} \, dx &=\int \left (b+\frac{a}{x^4}\right ) \, dx\\ &=-\frac{a}{3 x^3}+b x\\ \end{align*}
Mathematica [A] time = 0.0007711, size = 12, normalized size = 1. \[ b x-\frac{a}{3 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.9 \begin{align*} -{\frac{a}{3\,{x}^{3}}}+bx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.981826, size = 14, normalized size = 1.17 \begin{align*} b x - \frac{a}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40737, size = 31, normalized size = 2.58 \begin{align*} \frac{3 \, b x^{4} - a}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.233685, size = 8, normalized size = 0.67 \begin{align*} - \frac{a}{3 x^{3}} + b x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07053, size = 14, normalized size = 1.17 \begin{align*} b x - \frac{a}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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