Optimal. Leaf size=71 \[ -\frac {e \sqrt [3]{d+e x} F^{c \left (a-\frac {b d}{e}\right )} \Gamma \left (\frac {7}{3},-\frac {b c (d+e x) \log (F)}{e}\right )}{b^2 c^2 \log ^2(F) \sqrt [3]{-\frac {b c \log (F) (d+e x)}{e}}} \]
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Rubi [A] time = 0.03, antiderivative size = 71, 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 = {2181} \[ -\frac {e \sqrt [3]{d+e x} F^{c \left (a-\frac {b d}{e}\right )} \text {Gamma}\left (\frac {7}{3},-\frac {b c \log (F) (d+e x)}{e}\right )}{b^2 c^2 \log ^2(F) \sqrt [3]{-\frac {b c \log (F) (d+e x)}{e}}} \]
Antiderivative was successfully verified.
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Rule 2181
Rubi steps
\begin {align*} \int F^{c (a+b x)} (d+e x)^{4/3} \, dx &=-\frac {e F^{c \left (a-\frac {b d}{e}\right )} \sqrt [3]{d+e x} \Gamma \left (\frac {7}{3},-\frac {b c (d+e x) \log (F)}{e}\right )}{b^2 c^2 \log ^2(F) \sqrt [3]{-\frac {b c (d+e x) \log (F)}{e}}}\\ \end {align*}
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Mathematica [A] time = 0.08, size = 63, normalized size = 0.89 \[ -\frac {(d+e x)^{7/3} F^{c \left (a-\frac {b d}{e}\right )} \Gamma \left (\frac {7}{3},-\frac {b c (d+e x) \log (F)}{e}\right )}{e \left (-\frac {b c \log (F) (d+e x)}{e}\right )^{7/3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 117, normalized size = 1.65 \[ \frac {\frac {4 \, \left (-\frac {b c \log \relax (F)}{e}\right )^{\frac {2}{3}} e^{2} \Gamma \left (\frac {1}{3}, -\frac {{\left (b c e x + b c d\right )} \log \relax (F)}{e}\right )}{F^{\frac {b c d - a c e}{e}}} - 3 \, {\left (4 \, b c e \log \relax (F) - 3 \, {\left (b^{2} c^{2} e x + b^{2} c^{2} d\right )} \log \relax (F)^{2}\right )} {\left (e x + d\right )}^{\frac {1}{3}} F^{b c x + a c}}{9 \, b^{3} c^{3} \log \relax (F)^{3}} \]
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 \[ \int {\left (e x + d\right )}^{\frac {4}{3}} F^{{\left (b x + a\right )} c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.07, size = 0, normalized size = 0.00 \[ \int \left (e x +d \right )^{\frac {4}{3}} F^{\left (b x +a \right ) c}\, dx \]
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 \[ \int {\left (e x + d\right )}^{\frac {4}{3}} F^{{\left (b x + a\right )} c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \[ \int F^{c\,\left (a+b\,x\right )}\,{\left (d+e\,x\right )}^{4/3} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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