3.69.33 $\int (1+e^{e^{\frac{-1+5e^{16+x}+e^{16}x}{e^{16}}}+\frac{-1+5e^{16+x}+e^{16}x}{e^{16}}}(1+5e^x))dx$

Optimal. Leaf size=19 $$3+e^{e^{-\frac{1}{e^{16}}+5e^x+x}}+x$$

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Rubi [F]  time = 0.42, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}\int (1+\exp (e^{\frac{-1+5e^{16+x}+e^{16}x}{e^{16}}}+\frac{-1+5e^{16+x}+e^{16}x}{e^{16}})(1+5e^x))dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[1 + E^(E^((-1 + 5*E^(16 + x) + E^16*x)/E^16) + (-1 + 5*E^(16 + x) + E^16*x)/E^16)*(1 + 5*E^x),x]

[Out]

x + Defer[Subst][Defer[Int][E^(-E^(-16) + 5*x + E^(-E^(-16) + 5*x)*x), x], x, E^x] + 5*Defer[Subst][Defer[Int]
[E^(-E^(-16) + 5*x + E^(-E^(-16) + 5*x)*x)*x, x], x, E^x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =x+\int \exp (e^{\frac{-1+5e^{16+x}+e^{16}x}{e^{16}}}+\frac{-1+5e^{16+x}+e^{16}x}{e^{16}})(1+5e^x)dx\\ & =x+\int e^{-\frac{1}{e^{16}}+5e^x+e^{-\frac{1}{e^{16}}+5e^x+x}+x}(1+5e^x)dx\\ & =x+\mathrm{Subst}(\int e^{-\frac{1}{e^{16}}+5x+e^{-\frac{1}{e^{16}}+5x}x}(1+5x)dx,x,e^x)\\ & =x+\mathrm{Subst}(\int (e^{-\frac{1}{e^{16}}+5x+e^{-\frac{1}{e^{16}}+5x}x}+5e^{-\frac{1}{e^{16}}+5x+e^{-\frac{1}{e^{16}}+5x}x}x)dx,x,e^x)\\ & =x+5\mathrm{Subst}(\int e^{-\frac{1}{e^{16}}+5x+e^{-\frac{1}{e^{16}}+5x}x}xdx,x,e^x)+\mathrm{Subst}(\int e^{-\frac{1}{e^{16}}+5x+e^{-\frac{1}{e^{16}}+5x}x}dx,x,e^x)\end{array}\end{array}$$

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Mathematica [A]  time = 0.19, size = 18, normalized size = 0.95 $$\begin{array}{c}{e}^{e^{-\frac{1}{e^{16}}+5e^x+x}}+x\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[1 + E^(E^((-1 + 5*E^(16 + x) + E^16*x)/E^16) + (-1 + 5*E^(16 + x) + E^16*x)/E^16)*(1 + 5*E^x),x]

[Out]

E^E^(-E^(-16) + 5*E^x + x) + x

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fricas [B]  time = 0.49, size = 71, normalized size = 3.74 $$\begin{array}{c}(x{e}^{\left((x{e}^{16}+5e^{(x+16)}-1)e^{(-16)}\right)}+e^{\left((x{e}^{16}+e^{((x{e}^{16}+5e^{(x+16)}-1)e^{(-16)}+16)}+5e^{(x+16)}-1)e^{(-16)}\right)})e^{(-(x{e}^{16}+5e^{(x+16)}-1)e^{(-16)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*exp(x)+1)*exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(16))*exp(exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(
16)))+1,x, algorithm="fricas")

[Out]

(x*e^((x*e^16 + 5*e^(x + 16) - 1)*e^(-16)) + e^((x*e^16 + e^((x*e^16 + 5*e^(x + 16) - 1)*e^(-16) + 16) + 5*e^(
x + 16) - 1)*e^(-16)))*e^(-(x*e^16 + 5*e^(x + 16) - 1)*e^(-16))

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giac [A]  time = 0.19, size = 14, normalized size = 0.74 $$\begin{array}{c}x+e^{\left(e^{(x-e^{(-16)}+5e^x)}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*exp(x)+1)*exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(16))*exp(exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(
16)))+1,x, algorithm="giac")

[Out]

x + e^(e^(x - e^(-16) + 5*e^x))

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maple [A]  time = 0.18, size = 20, normalized size = 1.05

method	result	size
risch	$x+{\mathrm{e}}^{{\mathrm{e}}^{(5{\mathrm{e}}^{x+16}+x{\mathrm{e}}^{16}-1){\mathrm{e}}^{-16}}}$	$20$
default	$x+{\mathrm{e}}^{{\mathrm{e}}^{(5{\mathrm{e}}^{16}{\mathrm{e}}^x+x{\mathrm{e}}^{16}-1){\mathrm{e}}^{-16}}}$	$22$
norman	$x+{\mathrm{e}}^{{\mathrm{e}}^{(5{\mathrm{e}}^{16}{\mathrm{e}}^x+x{\mathrm{e}}^{16}-1){\mathrm{e}}^{-16}}}$	$22$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*exp(x)+1)*exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(16))*exp(exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(16)))+
1,x,method=_RETURNVERBOSE)

[Out]

x+exp(exp((5*exp(x+16)+x*exp(16)-1)*exp(-16)))

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maxima [A]  time = 0.63, size = 14, normalized size = 0.74 $$\begin{array}{c}x+e^{\left(e^{(x-e^{(-16)}+5e^x)}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*exp(x)+1)*exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(16))*exp(exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(
16)))+1,x, algorithm="maxima")

[Out]

x + e^(e^(x - e^(-16) + 5*e^x))

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mupad [B]  time = 4.15, size = 16, normalized size = 0.84 $$\begin{array}{c}x+{\mathrm{e}}^{{\mathrm{e}}^{-{\mathrm{e}}^{-16}}{\mathrm{e}}^{5{\mathrm{e}}^x}{\mathrm{e}}^x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(-16)*(x*exp(16) + 5*exp(16)*exp(x) - 1))*exp(exp(exp(-16)*(x*exp(16) + 5*exp(16)*exp(x) - 1)))*(5*
exp(x) + 1) + 1,x)

[Out]

x + exp(exp(-exp(-16))*exp(5*exp(x))*exp(x))

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sympy [A]  time = 0.34, size = 22, normalized size = 1.16 $$\begin{array}{c}x+e^{e^{\frac{x{e}^{16}+5e^{16}{e}^x-1}{e^{16}}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*exp(x)+1)*exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(16))*exp(exp((5*exp(16)*exp(x)+x*exp(16)-1)/exp(
16)))+1,x)

[Out]

x + exp(exp((x*exp(16) + 5*exp(16)*exp(x) - 1)*exp(-16)))

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