\(\int \frac {1}{8} e^{\frac {1}{8} (-96+24 e^{5 x}-x)} (-1+120 e^{5 x}) \, dx\) [9944]

Optimal result

Integrand size = 31, antiderivative size = 19 \[ \int \frac {1}{8} e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx=e^{-3 \left (4-e^{5 x}\right )-\frac {x}{8}} \]

[Out]

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

Rubi [A] (verified)

Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {12, 6838} \[ \int \frac {1}{8} e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx=e^{\frac {1}{8} \left (-x+24 e^{5 x}-96\right )} \]

[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 6838

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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84 \[ \int \frac {1}{8} e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx=e^{-12+3 e^{5 x}-\frac {x}{8}} \]

[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)

Maple [A] (verified)

Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68

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

[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)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {1}{8} e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx=e^{\left (-\frac {1}{8} \, x + 3 \, e^{\left (5 \, x\right )} - 12\right )} \]

[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)

Sympy [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {1}{8} e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx=e^{- \frac {x}{8} + 3 e^{5 x} - 12} \]

[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)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {1}{8} e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx=e^{\left (-\frac {1}{8} \, x + 3 \, e^{\left (5 \, x\right )} - 12\right )} \]

[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)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {1}{8} e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx=e^{\left (-\frac {1}{8} \, x + 3 \, e^{\left (5 \, x\right )} - 12\right )} \]

[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)

Mupad [B] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {1}{8} e^{\frac {1}{8} \left (-96+24 e^{5 x}-x\right )} \left (-1+120 e^{5 x}\right ) \, dx={\mathrm {e}}^{3\,{\mathrm {e}}^{5\,x}}\,{\mathrm {e}}^{-\frac {x}{8}}\,{\mathrm {e}}^{-12} \]

[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)