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

Optimal. Leaf size=11 \[ \frac {x}{\left (7-\frac {1}{e^4}\right )^2} \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.27, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {8} \begin {gather*} \frac {e^8 x}{\left (1-7 e^4\right )^2} \end {gather*}

Antiderivative was successfully verified.

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

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Mathematica [A]  time = 0.00, size = 19, normalized size = 1.73 \begin {gather*} \frac {e^8 x}{1-14 e^4+49 e^8} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(E^8*x)/(1 - 14*E^4 + 49*E^8)

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fricas [A]  time = 1.29, size = 16, normalized size = 1.45 \begin {gather*} \frac {x e^{8}}{49 \, e^{8} - 14 \, e^{4} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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giac [A]  time = 0.14, size = 16, normalized size = 1.45 \begin {gather*} \frac {x e^{8}}{49 \, e^{8} - 14 \, e^{4} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maple [A]  time = 0.02, size = 17, normalized size = 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	\(\frac {{\mathrm e}^{8} x}{49 \,{\mathrm e}^{8}-14 \,{\mathrm e}^{4}+1}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[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

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maxima [A]  time = 0.35, size = 16, normalized size = 1.45 \begin {gather*} \frac {x e^{8}}{49 \, e^{8} - 14 \, e^{4} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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mupad [B]  time = 0.00, size = 16, normalized size = 1.45 \begin {gather*} \frac {x\,{\mathrm {e}}^8}{49\,{\mathrm {e}}^8-14\,{\mathrm {e}}^4+1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.05, size = 15, normalized size = 1.36 \begin {gather*} \frac {x e^{8}}{- 14 e^{4} + 1 + 49 e^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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