Optimal. Leaf size=16 \[ \frac {f^{b x+c x^2}}{\log (f)} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2236} \[ \frac {f^{b x+c x^2}}{\log (f)} \]
Antiderivative was successfully verified.
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Rule 2236
Rubi steps
\begin {align*} \int f^{b x+c x^2} (b+2 c x) \, dx &=\frac {f^{b x+c x^2}}{\log (f)}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 16, normalized size = 1.00 \[ \frac {f^{b x+c x^2}}{\log (f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 16, normalized size = 1.00 \[ \frac {f^{c x^{2} + b x}}{\log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 16, normalized size = 1.00 \[ \frac {f^{c x^{2} + b x}}{\log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 17, normalized size = 1.06 \[ \frac {f^{c \,x^{2}+b x}}{\ln \relax (f )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 16, normalized size = 1.00 \[ \frac {f^{c x^{2} + b x}}{\log \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.52, size = 16, normalized size = 1.00 \[ \frac {f^{c\,x^2+b\,x}}{\ln \relax (f)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 22, normalized size = 1.38 \[ \begin {cases} \frac {f^{b x + c x^{2}}}{\log {\relax (f )}} & \text {for}\: \log {\relax (f )} \neq 0 \\b x + c x^{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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