Optimal. Leaf size=81 \[ \frac{2}{7} \left (9-e^x\right )^{7/2}-18 \left (9-e^x\right )^{5/2}+540 \left (9-e^x\right )^{3/2}-14580 \sqrt{9-e^x}-\frac{65610}{\sqrt{9-e^x}}+\frac{39366}{\left (9-e^x\right )^{3/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0819464, antiderivative size = 81, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{2}{7} \left (9-e^x\right )^{7/2}-18 \left (9-e^x\right )^{5/2}+540 \left (9-e^x\right )^{3/2}-14580 \sqrt{9-e^x}-\frac{65610}{\sqrt{9-e^x}}+\frac{39366}{\left (9-e^x\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[E^(6*x)/(9 - E^x)^(5/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.1197, size = 61, normalized size = 0.75 \[ \frac{2 \left (- e^{x} + 9\right )^{\frac{7}{2}}}{7} - 18 \left (- e^{x} + 9\right )^{\frac{5}{2}} + 540 \left (- e^{x} + 9\right )^{\frac{3}{2}} - 14580 \sqrt{- e^{x} + 9} - \frac{65610}{\sqrt{- e^{x} + 9}} + \frac{39366}{\left (- e^{x} + 9\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(6*x)/(9-exp(x))**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0439276, size = 48, normalized size = 0.59 \[ -\frac{2 \left (-839808 e^x+23328 e^{2 x}+432 e^{3 x}+18 e^{4 x}+e^{5 x}+5038848\right )}{7 \left (9-e^x\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[E^(6*x)/(9 - E^x)^(5/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 62, normalized size = 0.8 \[ 39366\, \left ( 9-{{\rm e}^{x}} \right ) ^{-3/2}+540\, \left ( 9-{{\rm e}^{x}} \right ) ^{3/2}-18\, \left ( 9-{{\rm e}^{x}} \right ) ^{5/2}+{\frac{2}{7} \left ( 9-{{\rm e}^{x}} \right ) ^{{\frac{7}{2}}}}-65610\,{\frac{1}{\sqrt{9-{{\rm e}^{x}}}}}-14580\,\sqrt{9-{{\rm e}^{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(6*x)/(9-exp(x))^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.786708, size = 82, normalized size = 1.01 \[ \frac{2}{7} \,{\left (-e^{x} + 9\right )}^{\frac{7}{2}} - 18 \,{\left (-e^{x} + 9\right )}^{\frac{5}{2}} + 540 \,{\left (-e^{x} + 9\right )}^{\frac{3}{2}} - 14580 \, \sqrt{-e^{x} + 9} - \frac{65610}{\sqrt{-e^{x} + 9}} + \frac{39366}{{\left (-e^{x} + 9\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(6*x)/(-e^x + 9)^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.23467, size = 59, normalized size = 0.73 \[ \frac{2 \,{\left (e^{\left (5 \, x\right )} + 18 \, e^{\left (4 \, x\right )} + 432 \, e^{\left (3 \, x\right )} + 23328 \, e^{\left (2 \, x\right )} - 839808 \, e^{x} + 5038848\right )}}{7 \,{\left (e^{x} - 9\right )} \sqrt{-e^{x} + 9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(6*x)/(-e^x + 9)^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{6 x}}{\left (- e^{x} + 9\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(6*x)/(9-exp(x))**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.232066, size = 101, normalized size = 1.25 \[ -\frac{2}{7} \,{\left (e^{x} - 9\right )}^{3} \sqrt{-e^{x} + 9} - 18 \,{\left (e^{x} - 9\right )}^{2} \sqrt{-e^{x} + 9} + 540 \,{\left (-e^{x} + 9\right )}^{\frac{3}{2}} - 14580 \, \sqrt{-e^{x} + 9} - \frac{13122 \,{\left (5 \, e^{x} - 42\right )}}{{\left (e^{x} - 9\right )} \sqrt{-e^{x} + 9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(6*x)/(-e^x + 9)^(5/2),x, algorithm="giac")
[Out]