Optimal. Leaf size=10 \[ b x-\frac {a}{x} \]
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Rubi [A] time = 0.00, antiderivative size = 10, 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} \begin {gather*} b x-\frac {a}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^2}{x^2} \, dx &=\int \left (b+\frac {a}{x^2}\right ) \, dx\\ &=-\frac {a}{x}+b x\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} b x-\frac {a}{x} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a+b x^2}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.06, size = 13, normalized size = 1.30 \begin {gather*} \frac {b x^{2} - a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 10, normalized size = 1.00 \begin {gather*} b x - \frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 1.10 \begin {gather*} b x -\frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 10, normalized size = 1.00 \begin {gather*} b x - \frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 10, normalized size = 1.00 \begin {gather*} b\,x-\frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 5, normalized size = 0.50 \begin {gather*} - \frac {a}{x} + b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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