3.89.51 $\int \frac{-x-e^{5+e^{5}x}x}{x}dx$

Optimal. Leaf size=23 $$3-e^{e^{5}x}-{(4+e^2)}^2-x$$

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.57, number of steps used = 3, number of rules used = 2, integrand size = 20, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.100, Rules used = {14, 2194} $$\begin{array}{c}-x-e^{e^{5}x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(-x - E^(5 + E^5*x)*x)/x,x]

[Out]

-E^(E^5*x) - x

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (-1-e^{5+e^{5}x})dx\\ & =-x-\int e^{5+e^{5}x}dx\\ & =-e^{e^{5}x}-x\end{array}\end{array}$$

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Mathematica [A]  time = 0.01, size = 13, normalized size = 0.57 $$\begin{array}{c}-e^{e^{5}x}-x\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-x - E^(5 + E^5*x)*x)/x,x]

[Out]

-E^(E^5*x) - x

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fricas [A]  time = 0.62, size = 23, normalized size = 1.00 $$\begin{array}{c}-\frac{(x^2{e}^5+e^{(x{e}^5+\log (x)+5)})e^{(-5)}}{x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(5+log(x))*exp(exp(5+log(x)))-x)/x,x, algorithm="fricas")

[Out]

-(x^2*e^5 + e^(x*e^5 + log(x) + 5))*e^(-5)/x

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giac [A]  time = 0.12, size = 11, normalized size = 0.48 $$\begin{array}{c}-x-e^{\left(x{e}^5\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(5+log(x))*exp(exp(5+log(x)))-x)/x,x, algorithm="giac")

[Out]

-x - e^(x*e^5)

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maple [A]  time = 0.04, size = 12, normalized size = 0.52

method	result	size
norman	$-x-{\mathrm{e}}^{x{\mathrm{e}}^5}$	$12$
risch	$-x-{\mathrm{e}}^{x{\mathrm{e}}^5}$	$12$
default	$-x-{\mathrm{e}}^{{\mathrm{e}}^{5+\ln (x)}}$	$13$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-exp(5+ln(x))*exp(exp(5+ln(x)))-x)/x,x,method=_RETURNVERBOSE)

[Out]

-x-exp(x*exp(5))

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maxima [A]  time = 0.36, size = 11, normalized size = 0.48 $$\begin{array}{c}-x-e^{\left(x{e}^5\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(5+log(x))*exp(exp(5+log(x)))-x)/x,x, algorithm="maxima")

[Out]

-x - e^(x*e^5)

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mupad [B]  time = 5.13, size = 11, normalized size = 0.48 $$\begin{array}{c}-x-{\mathrm{e}}^{x{\mathrm{e}}^5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x + exp(exp(log(x) + 5))*exp(log(x) + 5))/x,x)

[Out]

- x - exp(x*exp(5))

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sympy [A]  time = 0.09, size = 8, normalized size = 0.35 $$\begin{array}{c}-x-e^{x{e}^5}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(5+ln(x))*exp(exp(5+ln(x)))-x)/x,x)

[Out]

-x - exp(x*exp(5))

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