Optimal. Leaf size=20 \[ \frac {f^{a+b x^2}}{2 b \log (f)} \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2209} \[ \frac {f^{a+b x^2}}{2 b \log (f)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int f^{a+b x^2} x \, dx &=\frac {f^{a+b x^2}}{2 b \log (f)}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.00 \[ \frac {f^{a+b x^2}}{2 b \log (f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 18, normalized size = 0.90 \[ \frac {f^{b x^{2} + a}}{2 \, b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 18, normalized size = 0.90 \[ \frac {f^{b x^{2} + a}}{2 \, b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 19, normalized size = 0.95 \[ \frac {f^{b \,x^{2}+a}}{2 b \ln \relax (f )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 18, normalized size = 0.90 \[ \frac {f^{b x^{2} + a}}{2 \, b \log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.30, size = 18, normalized size = 0.90 \[ \frac {f^{b\,x^2+a}}{2\,b\,\ln \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 24, normalized size = 1.20 \[ \begin {cases} \frac {f^{a + b x^{2}}}{2 b \log {\relax (f )}} & \text {for}\: 2 b \log {\relax (f )} \neq 0 \\\frac {x^{2}}{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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