Optimal. Leaf size=27 \[ \frac {F^{a+b (c+d x)^3}}{3 b d \log (F)} \]
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Rubi [A] time = 0.07, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2209} \[ \frac {F^{a+b (c+d x)^3}}{3 b d \log (F)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^3} (c+d x)^2 \, dx &=\frac {F^{a+b (c+d x)^3}}{3 b d \log (F)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 1.00 \[ \frac {F^{a+b (c+d x)^3}}{3 b d \log (F)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 47, normalized size = 1.74 \[ \frac {F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}}{3 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 47, normalized size = 1.74 \[ \frac {F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a}}{3 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 48, normalized size = 1.78 \[ \frac {F^{b \,d^{3} x^{3}+3 b c \,d^{2} x^{2}+3 b \,c^{2} d x +b \,c^{3}+a}}{3 b d \ln \relax (F )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 25, normalized size = 0.93 \[ \frac {F^{{\left (d x + c\right )}^{3} b + a}}{3 \, b d \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.53, size = 25, normalized size = 0.93 \[ \frac {F^{a+b\,{\left (c+d\,x\right )}^3}}{3\,b\,d\,\ln \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 46, normalized size = 1.70 \[ \begin {cases} \frac {F^{a + b \left (c + d x\right )^{3}}}{3 b d \log {\relax (F )}} & \text {for}\: 3 b d \log {\relax (F )} \neq 0 \\c^{2} x + c d x^{2} + \frac {d^{2} x^{3}}{3} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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