Optimal. Leaf size=47 \[ -\frac {F^a (c+d x) \Gamma \left (\frac {1}{3},-b (c+d x)^3 \log (F)\right )}{3 d \sqrt [3]{-b \log (F) (c+d x)^3}} \]
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Rubi [A] time = 0.01, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2208} \[ -\frac {F^a (c+d x) \text {Gamma}\left (\frac {1}{3},-b \log (F) (c+d x)^3\right )}{3 d \sqrt [3]{-b \log (F) (c+d x)^3}} \]
Antiderivative was successfully verified.
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Rule 2208
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^3} \, dx &=-\frac {F^a (c+d x) \Gamma \left (\frac {1}{3},-b (c+d x)^3 \log (F)\right )}{3 d \sqrt [3]{-b (c+d x)^3 \log (F)}}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 47, normalized size = 1.00 \[ -\frac {F^a (c+d x) \Gamma \left (\frac {1}{3},-b (c+d x)^3 \log (F)\right )}{3 d \sqrt [3]{-b \log (F) (c+d x)^3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 63, normalized size = 1.34 \[ \frac {\left (-b d^{3} \log \relax (F)\right )^{\frac {2}{3}} F^{a} \Gamma \left (\frac {1}{3}, -{\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} \log \relax (F)\right )}{3 \, b d^{3} \log \relax (F)} \]
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 \[ \int F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.04, size = 0, normalized size = 0.00 \[ \int F^{a +\left (d x +c \right )^{3} b}\, dx \]
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 \[ \int F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \]
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 \[ \int F^{a+b\,{\left (c+d\,x\right )}^3} \,d x \]
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 \[ \int F^{a + b \left (c + d x\right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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