3.100.44 \(\int \frac {1}{8} e^{\frac {1}{8} (-96+24 e^{5 x}-x)} (-1+120 e^{5 x}) \, dx\)

Optimal. Leaf size=19 \[ e^{-3 \left (4-e^{5 x}\right )-\frac {x}{8}} \]

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Rubi [A]  time = 0.06, antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 2, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {12, 6706} \begin {gather*} e^{\frac {1}{8} \left (-x+24 e^{5 x}-96\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^((-96 + 24*E^(5*x) - x)/8)*(-1 + 120*E^(5*x)))/8,x]

[Out]

E^((-96 + 24*E^(5*x) - x)/8)

Rule 12

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

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx\\ &=e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 16, normalized size = 0.84 \begin {gather*} e^{-12+3 e^{5 x}-\frac {x}{8}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-96 + 24*E^(5*x) - x)/8)*(-1 + 120*E^(5*x)))/8,x]

[Out]

E^(-12 + 3*E^(5*x) - x/8)

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fricas [A]  time = 0.86, size = 12, normalized size = 0.63 \begin {gather*} e^{\left (-\frac {1}{8} \, x + 3 \, e^{\left (5 \, x\right )} - 12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/8*(120*exp(5*x)-1)*exp(3*exp(5*x)-1/8*x-12),x, algorithm="fricas")

[Out]

e^(-1/8*x + 3*e^(5*x) - 12)

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giac [A]  time = 0.39, size = 12, normalized size = 0.63 \begin {gather*} e^{\left (-\frac {1}{8} \, x + 3 \, e^{\left (5 \, x\right )} - 12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/8*(120*exp(5*x)-1)*exp(3*exp(5*x)-1/8*x-12),x, algorithm="giac")

[Out]

e^(-1/8*x + 3*e^(5*x) - 12)

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maple [A]  time = 0.05, size = 13, normalized size = 0.68

method	result	size
norman	\({\mathrm e}^{3 \,{\mathrm e}^{5 x}-\frac {x}{8}-12}\)	\(13\)
risch	\({\mathrm e}^{3 \,{\mathrm e}^{5 x}-\frac {x}{8}-12}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/8*(120*exp(5*x)-1)*exp(3*exp(5*x)-1/8*x-12),x,method=_RETURNVERBOSE)

[Out]

exp(3*exp(5*x)-1/8*x-12)

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maxima [A]  time = 0.35, size = 12, normalized size = 0.63 \begin {gather*} e^{\left (-\frac {1}{8} \, x + 3 \, e^{\left (5 \, x\right )} - 12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/8*(120*exp(5*x)-1)*exp(3*exp(5*x)-1/8*x-12),x, algorithm="maxima")

[Out]

e^(-1/8*x + 3*e^(5*x) - 12)

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mupad [B]  time = 0.08, size = 14, normalized size = 0.74 \begin {gather*} {\mathrm {e}}^{3\,{\mathrm {e}}^{5\,x}}\,{\mathrm {e}}^{-\frac {x}{8}}\,{\mathrm {e}}^{-12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(3*exp(5*x) - x/8 - 12)*(120*exp(5*x) - 1))/8,x)

[Out]

exp(3*exp(5*x))*exp(-x/8)*exp(-12)

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sympy [A]  time = 0.14, size = 12, normalized size = 0.63 \begin {gather*} e^{- \frac {x}{8} + 3 e^{5 x} - 12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/8*(120*exp(5*x)-1)*exp(3*exp(5*x)-1/8*x-12),x)

[Out]

exp(-x/8 + 3*exp(5*x) - 12)

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