Optimal. Leaf size=27 \[ \frac {F^{a+b (c+d x)^2}}{2 b d \log (F)} \]
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Rubi [A] time = 0.04, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2209} \[ \frac {F^{a+b (c+d x)^2}}{2 b d \log (F)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^2} (c+d x) \, dx &=\frac {F^{a+b (c+d x)^2}}{2 b d \log (F)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.00 \[ \frac {F^{a+b (c+d x)^2}}{2 b d \log (F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 35, normalized size = 1.30 \[ \frac {F^{b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a}}{2 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 35, normalized size = 1.30 \[ \frac {F^{b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a}}{2 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 1.33 \[ \frac {F^{b \,d^{2} x^{2}+2 b c d x +b \,c^{2}+a}}{2 b d \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.19, size = 25, normalized size = 0.93 \[ \frac {F^{{\left (d x + c\right )}^{2} b + a}}{2 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.52, size = 25, normalized size = 0.93 \[ \frac {F^{a+b\,{\left (c+d\,x\right )}^2}}{2\,b\,d\,\ln \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 36, normalized size = 1.33 \[ \begin {cases} \frac {F^{a + b \left (c + d x\right )^{2}}}{2 b d \log {\relax (F )}} & \text {for}\: 2 b d \log {\relax (F )} \neq 0 \\c x + \frac {d x^{2}}{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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