Optimal. Leaf size=69 \[ \frac {F^{c \left (a-\frac {b d}{e}\right )} (d+e x)^{-m} \Gamma \left (1-m,-\frac {b c (d+e x) \log (F)}{e}\right ) \left (-\frac {b c (d+e x) \log (F)}{e}\right )^m}{b c \log (F)} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 69, 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 = {2212}
\begin {gather*} \frac {(d+e x)^{-m} F^{c \left (a-\frac {b d}{e}\right )} \left (-\frac {b c \log (F) (d+e x)}{e}\right )^m \text {Gamma}\left (1-m,-\frac {b c \log (F) (d+e x)}{e}\right )}{b c \log (F)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2212
Rubi steps
\begin {align*} \int F^{c (a+b x)} (d+e x)^{-m} \, dx &=\frac {F^{c \left (a-\frac {b d}{e}\right )} (d+e x)^{-m} \Gamma \left (1-m,-\frac {b c (d+e x) \log (F)}{e}\right ) \left (-\frac {b c (d+e x) \log (F)}{e}\right )^m}{b c \log (F)}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 69, normalized size = 1.00 \begin {gather*} \frac {F^{c \left (a-\frac {b d}{e}\right )} (d+e x)^{-m} \Gamma \left (1-m,-\frac {b c (d+e x) \log (F)}{e}\right ) \left (-\frac {b c (d+e x) \log (F)}{e}\right )^m}{b c \log (F)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F]
time = 0.01, size = 0, normalized size = 0.00 \[\int F^{c \left (b x +a \right )} \left (e x +d \right )^{-m}\, dx\]
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 = 67, normalized size = 0.97 \begin {gather*} \frac {e^{\left ({\left (m e \log \left (-b c e^{\left (-1\right )} \log \left (F\right )\right ) - {\left (b c d - a c e\right )} \log \left (F\right )\right )} e^{\left (-1\right )}\right )} \Gamma \left (-m + 1, -{\left (b c x e + b c d\right )} e^{\left (-1\right )} \log \left (F\right )\right )}{b c \log \left (F\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \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 = -0.01 \begin {gather*} \int \frac {F^{c\,\left (a+b\,x\right )}}{{\left (d+e\,x\right )}^m} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________