Optimal. Leaf size=12 \[ b x-\frac {a}{2 x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 12, 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} \[ b x-\frac {a}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^3}{x^3} \, dx &=\int \left (b+\frac {a}{x^3}\right ) \, dx\\ &=-\frac {a}{2 x^2}+b x\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ b x-\frac {a}{2 x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 15, normalized size = 1.25 \[ \frac {2 \, b x^{3} - a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 10, normalized size = 0.83 \[ b x - \frac {a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.92 \[ b x -\frac {a}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 10, normalized size = 0.83 \[ b x - \frac {a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 10, normalized size = 0.83 \[ b\,x-\frac {a}{2\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 8, normalized size = 0.67 \[ - \frac {a}{2 x^{2}} + b x \]
Verification of antiderivative is not currently implemented for this CAS.
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