Optimal. Leaf size=47 \[ -\frac {F^a (c+d x) \Gamma \left (\frac {1}{3},-b (c+d x)^3 \log (F)\right )}{3 d \sqrt [3]{-b (c+d x)^3 \log (F)}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2239}
\begin {gather*} -\frac {F^a (c+d x) \text {Gamma}\left (\frac {1}{3},-b \log (F) (c+d x)^3\right )}{3 d \sqrt [3]{-b \log (F) (c+d x)^3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2239
Rubi steps
\begin {align*} \int F^{a+b (c+d x)^3} \, dx &=-\frac {F^a (c+d x) \Gamma \left (\frac {1}{3},-b (c+d x)^3 \log (F)\right )}{3 d \sqrt [3]{-b (c+d x)^3 \log (F)}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.09, size = 47, normalized size = 1.00 \begin {gather*} -\frac {F^a (c+d x) \Gamma \left (\frac {1}{3},-b (c+d x)^3 \log (F)\right )}{3 d \sqrt [3]{-b (c+d x)^3 \log (F)}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.00, size = 0, normalized size = 0.00 \[\int F^{a +b \left (d x +c \right )^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.11, size = 63, normalized size = 1.34 \begin {gather*} \frac {\left (-b d^{3} \log \left (F\right )\right )^{\frac {2}{3}} 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 )}{3 \, b d^{3} \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int F^{a + b \left (c + d x\right )^{3}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [F]
time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int F^{a+b\,{\left (c+d\,x\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________