Optimal. Leaf size=17 \[ \frac {b x^2}{2}-\frac {a}{2 x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, 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} \[ \frac {b x^2}{2}-\frac {a}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^4}{x^3} \, dx &=\int \left (\frac {a}{x^3}+b x\right ) \, dx\\ &=-\frac {a}{2 x^2}+\frac {b x^2}{2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {b x^2}{2}-\frac {a}{2 x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 14, normalized size = 0.82 \[ \frac {b x^{4} - a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 13, normalized size = 0.76 \[ \frac {1}{2} \, b x^{2} - \frac {a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \[ \frac {b \,x^{2}}{2}-\frac {a}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 13, normalized size = 0.76 \[ \frac {1}{2} \, b x^{2} - \frac {a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.76 \[ -\frac {a-b\,x^4}{2\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 12, normalized size = 0.71 \[ - \frac {a}{2 x^{2}} + \frac {b x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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