\(\int 2 e^4 x^7 \, dx\) [7733]

Optimal result

Integrand size = 8, antiderivative size = 10 \[ \int 2 e^4 x^7 \, dx=\frac {e^4 x^8}{4} \]

[Out]

1/4*x^8/exp(2)^4*exp(3)^4

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \[ \int 2 e^4 x^7 \, dx=\frac {e^4 x^8}{4} \]

[In]

Int[2*E^4*x^7,x]

[Out]

(E^4*x^8)/4

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps \begin{align*} \text {integral}& = \left (2 e^4\right ) \int x^7 \, dx \\ & = \frac {e^4 x^8}{4} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int 2 e^4 x^7 \, dx=\frac {e^4 x^8}{4} \]

[In]

Integrate[2*E^4*x^7,x]

[Out]

(E^4*x^8)/4

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80

method	result	size
risch	\(\frac {x^{8} {\mathrm e}^{4}}{4}\)	\(8\)
gosper	\(\frac {x^{8} {\mathrm e}^{-8} {\mathrm e}^{12}}{4}\)	\(14\)
default	\(\frac {x^{8} {\mathrm e}^{-8} {\mathrm e}^{12}}{4}\)	\(14\)
norman	\(\frac {x^{8} {\mathrm e}^{-8} {\mathrm e}^{12}}{4}\)	\(14\)
parallelrisch	\(\frac {x^{8} {\mathrm e}^{-8} {\mathrm e}^{12}}{4}\)	\(14\)

[In]

int(2*x^7*exp(3)^4/exp(2)^4,x,method=_RETURNVERBOSE)

[Out]

1/4*x^8*exp(4)

Fricas [A] (verification not implemented)

none

Time = 0.37 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int 2 e^4 x^7 \, dx=\frac {1}{4} \, x^{8} e^{4} \]

[In]

integrate(2*x^7*exp(3)^4/exp(2)^4,x, algorithm="fricas")

[Out]

1/4*x^8*e^4

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int 2 e^4 x^7 \, dx=\frac {x^{8} e^{4}}{4} \]

[In]

integrate(2*x**7*exp(3)**4/exp(2)**4,x)

[Out]

x**8*exp(4)/4

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int 2 e^4 x^7 \, dx=\frac {1}{4} \, x^{8} e^{4} \]

[In]

integrate(2*x^7*exp(3)^4/exp(2)^4,x, algorithm="maxima")

[Out]

1/4*x^8*e^4

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int 2 e^4 x^7 \, dx=\frac {1}{4} \, x^{8} e^{4} \]

[In]

integrate(2*x^7*exp(3)^4/exp(2)^4,x, algorithm="giac")

[Out]

1/4*x^8*e^4

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int 2 e^4 x^7 \, dx=\frac {x^8\,{\mathrm {e}}^4}{4} \]

[In]

int(2*x^7*exp(4),x)

[Out]

(x^8*exp(4))/4