Optimal. Leaf size=49 \[ -\frac{F^a (c+d x)^2 \text{Gamma}\left (\frac{2}{3},-b \log (F) (c+d x)^3\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{2/3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0411224, antiderivative size = 49, normalized size of antiderivative = 1., 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 = {2218} \[ -\frac{F^a (c+d x)^2 \text{Gamma}\left (\frac{2}{3},-b \log (F) (c+d x)^3\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{2/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2218
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*}
Mathematica [A] time = 0.0231367, size = 49, normalized size = 1. \[ -\frac{F^a (c+d x)^2 \text{Gamma}\left (\frac{2}{3},-b \log (F) (c+d x)^3\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{2/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.026, size = 0, normalized size = 0. \begin{align*} \int{F}^{a+b \left ( dx+c \right ) ^{3}} \left ( dx+c \right ) \, 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{\left (d x + c\right )} F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.58064, size = 157, normalized size = 3.2 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int F^{a + b \left (c + d x\right )^{3}} \left (c + d x\right )\, dx \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{\left (d x + c\right )} F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]