3.90.98 \(\int -8388608 e^{-10+6 e^{5 e^5}-8 x} \, dx\)

Optimal. Leaf size=27 \[ e^{6 \left (e^{5 e^5}-x\right )-2 x-10 (1-\log (4))} \]

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Rubi [A]  time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2194} \begin {gather*} 1048576 e^{-8 x-2 \left (5-3 e^{5 e^5}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-8388608*E^(-10 + 6*E^(5*E^5) - 8*x),x]

[Out]

1048576*E^(-2*(5 - 3*E^(5*E^5)) - 8*x)

Rule 12

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

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (8388608 \int e^{-10+6 e^{5 e^5}-8 x} \, dx\right )\\ &=1048576 e^{-2 \left (5-3 e^{5 e^5}\right )-8 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 18, normalized size = 0.67 \begin {gather*} 1048576 e^{-10+6 e^{5 e^5}-8 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-8388608*E^(-10 + 6*E^(5*E^5) - 8*x),x]

[Out]

1048576*E^(-10 + 6*E^(5*E^5) - 8*x)

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fricas [A]  time = 0.48, size = 17, normalized size = 0.63 \begin {gather*} e^{\left (-8 \, x + 6 \, e^{\left (5 \, e^{5}\right )} + 20 \, \log \relax (2) - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(3*exp(5*exp(5))+10*log(2)-4*x-5)^2,x, algorithm="fricas")

[Out]

e^(-8*x + 6*e^(5*e^5) + 20*log(2) - 10)

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giac [A]  time = 0.15, size = 17, normalized size = 0.63 \begin {gather*} e^{\left (-8 \, x + 6 \, e^{\left (5 \, e^{5}\right )} + 20 \, \log \relax (2) - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(3*exp(5*exp(5))+10*log(2)-4*x-5)^2,x, algorithm="giac")

[Out]

e^(-8*x + 6*e^(5*e^5) + 20*log(2) - 10)

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maple [A]  time = 0.02, size = 16, normalized size = 0.59

method	result	size
risch	\(1048576 \,{\mathrm e}^{6 \,{\mathrm e}^{5 \,{\mathrm e}^{5}}-10-8 x}\)	\(16\)
gosper	\(1048576 \,{\mathrm e}^{6 \,{\mathrm e}^{5 \,{\mathrm e}^{5}}-10-8 x}\)	\(20\)
derivativedivides	\(1048576 \,{\mathrm e}^{6 \,{\mathrm e}^{5 \,{\mathrm e}^{5}}-10-8 x}\)	\(20\)
default	\(1048576 \,{\mathrm e}^{6 \,{\mathrm e}^{5 \,{\mathrm e}^{5}}-10-8 x}\)	\(20\)
norman	\(1048576 \,{\mathrm e}^{6 \,{\mathrm e}^{5 \,{\mathrm e}^{5}}-10-8 x}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8*exp(3*exp(5*exp(5))+10*ln(2)-4*x-5)^2,x,method=_RETURNVERBOSE)

[Out]

1048576*exp(6*exp(5*exp(5))-10-8*x)

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maxima [A]  time = 0.35, size = 15, normalized size = 0.56 \begin {gather*} 1048576 \, e^{\left (-8 \, x + 6 \, e^{\left (5 \, e^{5}\right )} - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(3*exp(5*exp(5))+10*log(2)-4*x-5)^2,x, algorithm="maxima")

[Out]

1048576*e^(-8*x + 6*e^(5*e^5) - 10)

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mupad [B]  time = 7.02, size = 16, normalized size = 0.59 \begin {gather*} 1048576\,{\mathrm {e}}^{-8\,x}\,{\mathrm {e}}^{-10}\,{\mathrm {e}}^{6\,{\mathrm {e}}^{5\,{\mathrm {e}}^5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8*exp(6*exp(5*exp(5)) - 8*x + 20*log(2) - 10),x)

[Out]

1048576*exp(-8*x)*exp(-10)*exp(6*exp(5*exp(5)))

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sympy [A]  time = 0.09, size = 15, normalized size = 0.56 \begin {gather*} 1048576 e^{- 8 x - 10 + 6 e^{5 e^{5}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(3*exp(5*exp(5))+10*ln(2)-4*x-5)**2,x)

[Out]

1048576*exp(-8*x - 10 + 6*exp(5*exp(5)))

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