Optimal. Leaf size=15 \[ \frac {1}{2} f^a \text {Ei}\left (b x^2 \log (f)\right ) \]
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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} \[ \frac {1}{2} f^a \text {Ei}\left (b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
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Rule 2210
Rubi steps
\begin {align*} \int \frac {f^{a+b x^2}}{x} \, dx &=\frac {1}{2} f^a \text {Ei}\left (b x^2 \log (f)\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {1}{2} f^a \text {Ei}\left (b x^2 \log (f)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 13, normalized size = 0.87 \[ \frac {1}{2} \, f^{a} {\rm Ei}\left (b x^{2} \log \relax (f)\right ) \]
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 \[ \int \frac {f^{b x^{2} + a}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 1.07 \[ -\frac {f^{a} \Ei \left (1, -b \,x^{2} \ln \relax (f )\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 13, normalized size = 0.87 \[ \frac {1}{2} \, f^{a} {\rm Ei}\left (b x^{2} \log \relax (f)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.18, size = 13, normalized size = 0.87 \[ \frac {f^a\,\mathrm {ei}\left (b\,x^2\,\ln \relax (f)\right )}{2} \]
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 \[ \int \frac {f^{a + b x^{2}}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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