Optimal. Leaf size=49 \[ -\frac {F^a (c+d x)^2 \Gamma \left (\frac {2}{3},-b (c+d x)^3 \log (F)\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{2/3}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 49, 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 = {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 = 0.02, size = 49, normalized size = 1.00 \[ -\frac {F^a (c+d x)^2 \Gamma \left (\frac {2}{3},-b (c+d x)^3 \log (F)\right )}{3 d \left (-b \log (F) (c+d x)^3\right )^{2/3}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.43, size = 63, normalized size = 1.29 \[ \frac {\left (-b d^{3} \log \relax (F)\right )^{\frac {1}{3}} F^{a} \Gamma \left (\frac {2}{3}, -{\left (b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3}\right )} \log \relax (F)\right )}{3 \, b d^{2} \log \relax (F)} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (d x + c\right )} F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.06, size = 0, normalized size = 0.00 \[ \int \left (d x +c \right ) F^{a +\left (d x +c \right )^{3} b}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (d x + c\right )} F^{{\left (d x + c\right )}^{3} b + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.02 \[ \int F^{a+b\,{\left (c+d\,x\right )}^3}\,\left (c+d\,x\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int F^{a + b \left (c + d x\right )^{3}} \left (c + d x\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________