Optimal. Leaf size=15 \[ -\frac {1}{2} f^a \text {Ei}\left (\frac {b \log (f)}{x^2}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2210} \[ -\frac {1}{2} f^a \text {Ei}\left (\frac {b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^2}}}{x} \, dx &=-\frac {1}{2} f^a \text {Ei}\left (\frac {b \log (f)}{x^2}\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ -\frac {1}{2} f^a \text {Ei}\left (\frac {b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 13, normalized size = 0.87 \[ -\frac {1}{2} \, f^{a} {\rm Ei}\left (\frac {b \log \relax (f)}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{a + \frac {b}{x^{2}}}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 1.07 \[ \frac {f^{a} \Ei \left (1, -\frac {b \ln \relax (f )}{x^{2}}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.25, size = 13, normalized size = 0.87 \[ -\frac {1}{2} \, f^{a} {\rm Ei}\left (\frac {b \log \relax (f)}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 13, normalized size = 0.87 \[ -\frac {f^a\,\mathrm {ei}\left (\frac {b\,\ln \relax (f)}{x^2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{a + \frac {b}{x^{2}}}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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