Optimal. Leaf size=49 \[ -\frac {F^a (c+d x)^2 \Gamma \left (\frac {2}{3},-b (c+d x)^3 \log (F)\right )}{3 d \left (-b (c+d x)^3 \log (F)\right )^{2/3}} \]
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Rubi [A]
time = 0.03, antiderivative size = 49, 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 = {2250}
\begin {gather*} -\frac {F^a (c+d x)^2 \text {Gamma}\left (\frac {2}{3},-b \log (F) (c+d x)^3\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{2/3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2250
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^3} (c+d x) \, dx &=-\frac {F^a (c+d x)^2 \Gamma \left (\frac {2}{3},-b (c+d x)^3 \log (F)\right )}{3 d \left (-b (c+d x)^3 \log (F)\right )^{2/3}}\\ \end {align*}
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Mathematica [A]
time = 0.16, size = 49, normalized size = 1.00 \begin {gather*} -\frac {F^a (c+d x)^2 \Gamma \left (\frac {2}{3},-b (c+d x)^3 \log (F)\right )}{3 d \left (-b (c+d x)^3 \log (F)\right )^{2/3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.01, size = 0, normalized size = 0.00 \[\int F^{a +b \left (d x +c \right )^{3}} \left (d x +c \right )\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.10, size = 63, normalized size = 1.29 \begin {gather*} \frac {\left (-b d^{3} \log \left (F\right )\right )^{\frac {1}{3}} F^{a} \Gamma \left (\frac {2}{3}, -{\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} \log \left (F\right )\right )}{3 \, b d^{2} \log \left (F\right )} \end {gather*}
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 \begin {gather*} \int F^{a + b \left (c + d x\right )^{3}} \left (c + d x\right )\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int F^{a+b\,{\left (c+d\,x\right )}^3}\,\left (c+d\,x\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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