Optimal. Leaf size=61 \[ \frac{F^a (c+d x)^{m+1} \left (-\frac{b \log (F)}{(c+d x)^3}\right )^{\frac{m+1}{3}} \text{Gamma}\left (\frac{1}{3} (-m-1),-\frac{b \log (F)}{(c+d x)^3}\right )}{3 d} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0764817, antiderivative size = 61, 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 \[ \frac{F^a (c+d x)^{m+1} \left (-\frac{b \log (F)}{(c+d x)^3}\right )^{\frac{m+1}{3}} \text{Gamma}\left (\frac{1}{3} (-m-1),-\frac{b \log (F)}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b/(c + d*x)^3)*(c + d*x)^m,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.09703, size = 56, normalized size = 0.92 \[ \frac{F^{a} \left (- \frac{b \log{\left (F \right )}}{\left (c + d x\right )^{3}}\right )^{\frac{m}{3} + \frac{1}{3}} \left (c + d x\right )^{m + 1} \Gamma{\left (- \frac{m}{3} - \frac{1}{3},- \frac{b \log{\left (F \right )}}{\left (c + d x\right )^{3}} \right )}}{3 d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b/(d*x+c)**3)*(d*x+c)**m,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0695781, size = 61, normalized size = 1. \[ \frac{F^a (c+d x)^{m+1} \left (-\frac{b \log (F)}{(c+d x)^3}\right )^{\frac{m+1}{3}} \text{Gamma}\left (\frac{1}{3} (-m-1),-\frac{b \log (F)}{(c+d x)^3}\right )}{3 d} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b/(c + d*x)^3)*(c + d*x)^m,x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.108, size = 0, normalized size = 0. \[ \int{F}^{a+{\frac{b}{ \left ( dx+c \right ) ^{3}}}} \left ( dx+c \right ) ^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b/(d*x+c)^3)*(d*x+c)^m,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (d x + c\right )}^{m} F^{a + \frac{b}{{\left (d x + c\right )}^{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^m*F^(a + b/(d*x + c)^3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (d x + c\right )}^{m} F^{\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^m*F^(a + b/(d*x + c)^3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(a+b/(d*x+c)**3)*(d*x+c)**m,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (d x + c\right )}^{m} F^{a + \frac{b}{{\left (d x + c\right )}^{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^m*F^(a + b/(d*x + c)^3),x, algorithm="giac")
[Out]