\(\int \frac {e^8}{1-14 e^4+49 e^8} \, dx\) [7642]

Optimal result

Integrand size = 18, antiderivative size = 11 \[ \int \frac {e^8}{1-14 e^4+49 e^8} \, dx=\frac {x}{\left (7-\frac {1}{e^4}\right )^2} \]

[Out]

x/(7-exp(-1)^4)^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.27, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {8} \[ \int \frac {e^8}{1-14 e^4+49 e^8} \, dx=\frac {e^8 x}{\left (1-7 e^4\right )^2} \]

[In]

Int[E^8/(1 - 14*E^4 + 49*E^8),x]

[Out]

(E^8*x)/(1 - 7*E^4)^2

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps \begin{align*} \text {integral}& = \frac {e^8 x}{\left (1-7 e^4\right )^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.73 \[ \int \frac {e^8}{1-14 e^4+49 e^8} \, dx=\frac {e^8 x}{1-14 e^4+49 e^8} \]

[In]

Integrate[E^8/(1 - 14*E^4 + 49*E^8),x]

[Out]

(E^8*x)/(1 - 14*E^4 + 49*E^8)

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.55

method	result	size
norman	\(\frac {{\mathrm e}^{8} x}{\left (7 \,{\mathrm e}^{4}-1\right )^{2}}\)	\(17\)
risch	\(\frac {{\mathrm e}^{8} x}{49 \,{\mathrm e}^{8}-14 \,{\mathrm e}^{4}+1}\)	\(17\)
default	\(\frac {{\mathrm e}^{8} x}{49 \,{\mathrm e}^{8}-14 \,{\mathrm e}^{4}+1}\)	\(23\)
parallelrisch	\(\frac {{\mathrm e}^{8} x}{49 \,{\mathrm e}^{8}-14 \,{\mathrm e}^{4}+1}\)	\(23\)

[In]

int(exp(1)^8/(49*exp(1)^8-14*exp(1)^4+1),x,method=_RETURNVERBOSE)

[Out]

exp(1)^8/(7*exp(1)^4-1)^2*x

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.45 \[ \int \frac {e^8}{1-14 e^4+49 e^8} \, dx=\frac {x e^{8}}{49 \, e^{8} - 14 \, e^{4} + 1} \]

[In]

integrate(exp(1)^8/(49*exp(1)^8-14*exp(1)^4+1),x, algorithm="fricas")

[Out]

x*e^8/(49*e^8 - 14*e^4 + 1)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.36 \[ \int \frac {e^8}{1-14 e^4+49 e^8} \, dx=\frac {x e^{8}}{- 14 e^{4} + 1 + 49 e^{8}} \]

[In]

integrate(exp(1)**8/(49*exp(1)**8-14*exp(1)**4+1),x)

[Out]

x*exp(8)/(-14*exp(4) + 1 + 49*exp(8))

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.45 \[ \int \frac {e^8}{1-14 e^4+49 e^8} \, dx=\frac {x e^{8}}{49 \, e^{8} - 14 \, e^{4} + 1} \]

[In]

integrate(exp(1)^8/(49*exp(1)^8-14*exp(1)^4+1),x, algorithm="maxima")

[Out]

x*e^8/(49*e^8 - 14*e^4 + 1)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.45 \[ \int \frac {e^8}{1-14 e^4+49 e^8} \, dx=\frac {x e^{8}}{49 \, e^{8} - 14 \, e^{4} + 1} \]

[In]

integrate(exp(1)^8/(49*exp(1)^8-14*exp(1)^4+1),x, algorithm="giac")

[Out]

x*e^8/(49*e^8 - 14*e^4 + 1)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.45 \[ \int \frac {e^8}{1-14 e^4+49 e^8} \, dx=\frac {x\,{\mathrm {e}}^8}{49\,{\mathrm {e}}^8-14\,{\mathrm {e}}^4+1} \]

[In]

int(exp(8)/(49*exp(8) - 14*exp(4) + 1),x)

[Out]

(x*exp(8))/(49*exp(8) - 14*exp(4) + 1)