Optimal. Leaf size=49 \[ -\frac{F^a \left (-b \log (F) (c+d x)^3\right )^{2/3} \text{Gamma}\left (-\frac{2}{3},-b \log (F) (c+d x)^3\right )}{3 d (c+d x)^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0629146, antiderivative size = 49, 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} \[ -\frac{F^a \left (-b \log (F) (c+d x)^3\right )^{2/3} \text{Gamma}\left (-\frac{2}{3},-b \log (F) (c+d x)^3\right )}{3 d (c+d x)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
Rubi steps
\begin{align*} \int \frac{F^{a+b (c+d x)^3}}{(c+d x)^3} \, dx &=-\frac{F^a \Gamma \left (-\frac{2}{3},-b (c+d x)^3 \log (F)\right ) \left (-b (c+d x)^3 \log (F)\right )^{2/3}}{3 d (c+d x)^2}\\ \end{align*}
Mathematica [A] time = 0.0165271, size = 49, normalized size = 1. \[ -\frac{F^a \left (-b \log (F) (c+d x)^3\right )^{2/3} \text{Gamma}\left (-\frac{2}{3},-b \log (F) (c+d x)^3\right )}{3 d (c+d x)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.044, size = 0, normalized size = 0. \begin{align*} \int{\frac{{F}^{a+b \left ( dx+c \right ) ^{3}}}{ \left ( dx+c \right ) ^{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F^{{\left (d x + c\right )}^{3} b + a}}{{\left (d x + c\right )}^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.5409, size = 301, normalized size = 6.14 \begin{align*} \frac{\left (-b d^{3} \log \left (F\right )\right )^{\frac{2}{3}}{\left (d^{2} x^{2} + 2 \, c d x + c^{2}\right )} 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 \left (F\right )\right ) - F^{b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a} d^{2}}{2 \,{\left (d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{F^{{\left (d x + c\right )}^{3} b + a}}{{\left (d x + c\right )}^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]