3.73.23 $\int e^{e^{\frac{1}{2}(e^{e^{4}x}+2x)}+\frac{1}{2}(e^{e^{4}x}+2x)}(26+13e^{4+e^{4}x})dx$

Optimal. Leaf size=19 $$26e^{e^{\frac{e^{e^{4}x}}{2}+x}}$$

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Rubi [F]  time = 0.46, 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 = {} $$\begin{array}{c}\int \exp (e^{\frac{1}{2}(e^{e^{4}x}+2x)}+\frac{1}{2}(e^{e^{4}x}+2x))(26+13e^{4+e^{4}x})dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[E^(E^((E^(E^4*x) + 2*x)/2) + (E^(E^4*x) + 2*x)/2)*(26 + 13*E^(4 + E^4*x)),x]

[Out]

26*Defer[Int][E^((E^(E^4*x) + 2*E^(E^(E^4*x)/2 + x) + 2*x)/2), x] + 13*Defer[Int][E^((8 + E^(E^4*x) + 2*E^(E^(
E^4*x)/2 + x) + 2*(1 + E^4)*x)/2), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int 13e^{\frac{1}{2}(e^{e^{4}x}+2e^{\frac{e^{e^{4}x}}{2}+x}+2x)}(2+e^{4+e^{4}x})dx\\ & =13\int e^{\frac{1}{2}(e^{e^{4}x}+2e^{\frac{e^{e^{4}x}}{2}+x}+2x)}(2+e^{4+e^{4}x})dx\\ & =13\int (2e^{\frac{1}{2}(e^{e^{4}x}+2e^{\frac{e^{e^{4}x}}{2}+x}+2x)}+\exp (4+e^{4}x+\frac{1}{2}(e^{e^{4}x}+2e^{\frac{e^{e^{4}x}}{2}+x}+2x)))dx\\ & =13\int \exp (4+e^{4}x+\frac{1}{2}(e^{e^{4}x}+2e^{\frac{e^{e^{4}x}}{2}+x}+2x))dx+26\int e^{\frac{1}{2}(e^{e^{4}x}+2e^{\frac{e^{e^{4}x}}{2}+x}+2x)}dx\\ & =13\int \exp \left(\frac{1}{2}(8+e^{e^{4}x}+2e^{\frac{e^{e^{4}x}}{2}+x}+2(1+e^4)x)\right)dx+26\int e^{\frac{1}{2}(e^{e^{4}x}+2e^{\frac{e^{e^{4}x}}{2}+x}+2x)}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.15, size = 19, normalized size = 1.00 $$\begin{array}{c}26e^{e^{\frac{e^{e^{4}x}}{2}+x}}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[E^(E^((E^(E^4*x) + 2*x)/2) + (E^(E^4*x) + 2*x)/2)*(26 + 13*E^(4 + E^4*x)),x]

[Out]

26*E^E^(E^(E^4*x)/2 + x)

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fricas [B]  time = 0.70, size = 60, normalized size = 3.16 $$\begin{array}{c}26e^{(\frac{1}{2}(2x{e}^4+e^{(x{e}^4+4)}+2e^{(\frac{1}{2}(2x{e}^4+e^{(x{e}^4+4)})e^{(-4)}+4)})e^{(-4)}-\frac{1}{2}(2x{e}^4+e^{(x{e}^4+4)})e^{(-4)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((13*exp(4)*exp(x*exp(4))+26)*exp(1/2*exp(x*exp(4))+x)*exp(exp(1/2*exp(x*exp(4))+x)),x, algorithm="fr
icas")

[Out]

26*e^(1/2*(2*x*e^4 + e^(x*e^4 + 4) + 2*e^(1/2*(2*x*e^4 + e^(x*e^4 + 4))*e^(-4) + 4))*e^(-4) - 1/2*(2*x*e^4 + e
^(x*e^4 + 4))*e^(-4))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\int 13(e^{(x{e}^4+4)}+2)e^{(x+\frac{1}{2}{e}^{\left(x{e}^4\right)}+e^{(x+\frac{1}{2}{e}^{\left(x{e}^4\right)})})}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((13*exp(4)*exp(x*exp(4))+26)*exp(1/2*exp(x*exp(4))+x)*exp(exp(1/2*exp(x*exp(4))+x)),x, algorithm="gi
ac")

[Out]

integrate(13*(e^(x*e^4 + 4) + 2)*e^(x + 1/2*e^(x*e^4) + e^(x + 1/2*e^(x*e^4))), x)

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maple [A]  time = 0.11, size = 14, normalized size = 0.74

method	result	size
norman	$26{\mathrm{e}}^{{\mathrm{e}}^{\frac{{\mathrm{e}}^{x{\mathrm{e}}^4}}{2}+x}}$	$14$
risch	$26{\mathrm{e}}^{{\mathrm{e}}^{\frac{{\mathrm{e}}^{x{\mathrm{e}}^4}}{2}+x}}$	$14$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((13*exp(4)*exp(x*exp(4))+26)*exp(1/2*exp(x*exp(4))+x)*exp(exp(1/2*exp(x*exp(4))+x)),x,method=_RETURNVERBOS
E)

[Out]

26*exp(exp(1/2*exp(x*exp(4))+x))

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maxima [A]  time = 0.48, size = 13, normalized size = 0.68 $$\begin{array}{c}26e^{\left(e^{(x+\frac{1}{2}{e}^{\left(x{e}^4\right)})}\right)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((13*exp(4)*exp(x*exp(4))+26)*exp(1/2*exp(x*exp(4))+x)*exp(exp(1/2*exp(x*exp(4))+x)),x, algorithm="ma
xima")

[Out]

26*e^(e^(x + 1/2*e^(x*e^4)))

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mupad [B]  time = 0.20, size = 14, normalized size = 0.74 $$\begin{array}{c}26{\mathrm{e}}^{{\mathrm{e}}^{\frac{{\mathrm{e}}^{x{\mathrm{e}}^4}}{2}}{\mathrm{e}}^x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x + exp(x*exp(4))/2)*exp(exp(x + exp(x*exp(4))/2))*(13*exp(4)*exp(x*exp(4)) + 26),x)

[Out]

26*exp(exp(exp(x*exp(4))/2)*exp(x))

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sympy [A]  time = 0.40, size = 14, normalized size = 0.74 $$\begin{array}{c}26e^{e^{x+\frac{e^{x{e}^4}}{2}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((13*exp(4)*exp(x*exp(4))+26)*exp(1/2*exp(x*exp(4))+x)*exp(exp(1/2*exp(x*exp(4))+x)),x)

[Out]

26*exp(exp(x + exp(x*exp(4))/2))

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