Optimal. Leaf size=37 \[ -\frac{x e^{a+c} \left (-(b+d) x^n\right )^{-1/n} \text{Gamma}\left (\frac{1}{n},-(b+d) x^n\right )}{n} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0629906, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{x e^{a+c} \left (-(b+d) x^n\right )^{-1/n} \text{Gamma}\left (\frac{1}{n},-(b+d) x^n\right )}{n} \]
Antiderivative was successfully verified.
[In] Int[E^(a + c + b*x^n + d*x^n),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int e^{a + b x^{n} + c + d x^{n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(a+c+b*x**n+d*x**n),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.021157, size = 0, normalized size = 0. \[ \int e^{a+c+b x^n+d x^n} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[E^(a + c + b*x^n + d*x^n),x]
[Out]
_______________________________________________________________________________________
Maple [C] time = 0.05, size = 241, normalized size = 6.5 \[{\frac{{{\rm e}^{a+c}}}{n} \left ( -b-d \right ) ^{-{n}^{-1}} \left ({\frac{{n}^{2}{x}^{-n+1} \left ( -b-d \right ) ^{{n}^{-1}-1} \left ( n{x}^{n} \left ( -b-d \right ) +n+1 \right ) }{ \left ( 1+n \right ) \left ( 1+2\,n \right ) } \left ({x}^{n} \left ( -b-d \right ) \right ) ^{-{\frac{1+n}{2\,n}}}{{\rm e}^{-{\frac{{x}^{n} \left ( -b-d \right ) }{2}}}}{{\sl M}_{{n}^{-1}-{\frac{1+n}{2\,n}},\,{\frac{1+n}{2\,n}}+{\frac{1}{2}}}\left ({x}^{n} \left ( -b-d \right ) \right )}}+{\frac{n{x}^{-n+1} \left ( -b-d \right ) ^{{n}^{-1}-1} \left ( 1+n \right ) }{1+2\,n} \left ({x}^{n} \left ( -b-d \right ) \right ) ^{-{\frac{1+n}{2\,n}}}{{\rm e}^{-{\frac{{x}^{n} \left ( -b-d \right ) }{2}}}}{{\sl M}_{{n}^{-1}-{\frac{1+n}{2\,n}}+1,\,{\frac{1+n}{2\,n}}+{\frac{1}{2}}}\left ({x}^{n} \left ( -b-d \right ) \right )}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(a+c+b*x^n+d*x^n),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.06941, size = 49, normalized size = 1.32 \[ -\frac{x e^{\left (a + c\right )} \Gamma \left (\frac{1}{n}, -{\left (b + d\right )} x^{n}\right )}{\left (-{\left (b + d\right )} x^{n}\right )^{\left (\frac{1}{n}\right )} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(b*x^n + d*x^n + a + c),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (e^{\left ({\left (b + d\right )} x^{n} + a + c\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(b*x^n + d*x^n + a + c),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ e^{a} e^{c} \int e^{b x^{n}} e^{d x^{n}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(a+c+b*x**n+d*x**n),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int e^{\left (b x^{n} + d x^{n} + a + c\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(b*x^n + d*x^n + a + c),x, algorithm="giac")
[Out]