Optimal. Leaf size=31 \[ \frac{b^4 F^a \log ^4(F) \text{Gamma}\left (-4,-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
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Rubi [A] time = 0.0505083, antiderivative size = 31, normalized size of antiderivative = 1., 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 = {2218} \[ \frac{b^4 F^a \log ^4(F) \text{Gamma}\left (-4,-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
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Rule 2218
Rubi steps
\begin{align*} \int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^7 \, dx &=\frac{b^4 F^a \Gamma \left (-4,-\frac{b \log (F)}{(c+d x)^2}\right ) \log ^4(F)}{2 d}\\ \end{align*}
Mathematica [A] time = 0.0075925, size = 31, normalized size = 1. \[ \frac{b^4 F^a \log ^4(F) \text{Gamma}\left (-4,-\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.064, size = 646, normalized size = 20.8 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{1}{48} \,{\left (6 \, F^{a} d^{7} x^{8} + 48 \, F^{a} c d^{6} x^{7} + 2 \,{\left (84 \, F^{a} c^{2} d^{5} + F^{a} b d^{5} \log \left (F\right )\right )} x^{6} + 12 \,{\left (28 \, F^{a} c^{3} d^{4} + F^{a} b c d^{4} \log \left (F\right )\right )} x^{5} +{\left (420 \, F^{a} c^{4} d^{3} + 30 \, F^{a} b c^{2} d^{3} \log \left (F\right ) + F^{a} b^{2} d^{3} \log \left (F\right )^{2}\right )} x^{4} + 4 \,{\left (84 \, F^{a} c^{5} d^{2} + 10 \, F^{a} b c^{3} d^{2} \log \left (F\right ) + F^{a} b^{2} c d^{2} \log \left (F\right )^{2}\right )} x^{3} +{\left (168 \, F^{a} c^{6} d + 30 \, F^{a} b c^{4} d \log \left (F\right ) + 6 \, F^{a} b^{2} c^{2} d \log \left (F\right )^{2} + F^{a} b^{3} d \log \left (F\right )^{3}\right )} x^{2} + 2 \,{\left (24 \, F^{a} c^{7} + 6 \, F^{a} b c^{5} \log \left (F\right ) + 2 \, F^{a} b^{2} c^{3} \log \left (F\right )^{2} + F^{a} b^{3} c \log \left (F\right )^{3}\right )} x\right )} F^{\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}} + \int \frac{{\left (F^{a} b^{4} d^{2} x^{2} \log \left (F\right )^{4} + 2 \, F^{a} b^{4} c d x \log \left (F\right )^{4} - 6 \, F^{a} b c^{8} \log \left (F\right ) - 2 \, F^{a} b^{2} c^{6} \log \left (F\right )^{2} - F^{a} b^{3} c^{4} \log \left (F\right )^{3}\right )} F^{\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}}}{24 \,{\left (d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (d x + c\right )}^{7} F^{a + \frac{b}{{\left (d x + c\right )}^{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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