3.85.75 $\int \frac{e^{e^{-\frac{2x}{1+e^8}}(12-x)-\frac{2x}{1+e^8}}(-25-e^8+2x)}{1+e^8}dx$

Optimal. Leaf size=20 $$e^{e^{-\frac{2x}{1+e^8}}(12-x)}$$

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Rubi [F]  time = 0.48, 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 = {} $$\begin{array}{c}\int \frac{e^{e^{-\frac{2x}{1+e^8}}(12-x)-\frac{2x}{1+e^8}}(-25-e^8+2x)}{1+e^8}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^((12 - x)/E^((2*x)/(1 + E^8)) - (2*x)/(1 + E^8))*(-25 - E^8 + 2*x))/(1 + E^8),x]

[Out]

-(((25 + E^8)*Defer[Int][E^((12 - x)/E^((2*x)/(1 + E^8)) - (2*x)/(1 + E^8)), x])/(1 + E^8)) + (2*Defer[Int][E^
((12 - x)/E^((2*x)/(1 + E^8)) - (2*x)/(1 + E^8))*x, x])/(1 + E^8)

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{\int e^{e^{-\frac{2x}{1+e^8}}(12-x)-\frac{2x}{1+e^8}}(-25-e^8+2x)dx}{1+e^8}\\ & =\frac{\int (-25e^{e^{-\frac{2x}{1+e^8}}(12-x)-\frac{2x}{1+e^8}}(1+\frac{e^8}{25})+2e^{e^{-\frac{2x}{1+e^8}}(12-x)-\frac{2x}{1+e^8}}x)dx}{1+e^8}\\ & =\frac{2\int e^{e^{-\frac{2x}{1+e^8}}(12-x)-\frac{2x}{1+e^8}}xdx}{1+e^8}-\frac{(25+e^8)\int e^{e^{-\frac{2x}{1+e^8}}(12-x)-\frac{2x}{1+e^8}}dx}{1+e^8}\end{array}\end{array}$$

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Mathematica [A]  time = 0.24, size = 35, normalized size = 1.75 $$\begin{array}{c}-\frac{e^{-e^{-\frac{2x}{1+e^8}}(-12+x)}(-1-e^8)}{1+e^8}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^((12 - x)/E^((2*x)/(1 + E^8)) - (2*x)/(1 + E^8))*(-25 - E^8 + 2*x))/(1 + E^8),x]

[Out]

-((-1 - E^8)/(E^((-12 + x)/E^((2*x)/(1 + E^8)))*(1 + E^8)))

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fricas [B]  time = 0.64, size = 43, normalized size = 2.15 $$\begin{array}{c}{e}^{(-\frac{((x-12)e^8+x-12)e^{(-\frac{2x}{e^8+1})}+2x}{e^8+1}+\frac{2x}{e^8+1})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(2)^4+2*x-25)*exp((12-x)/exp(2*x/(exp(2)^4+1)))/(exp(2)^4+1)/exp(2*x/(exp(2)^4+1)),x, algorithm
="fricas")

[Out]

e^(-(((x - 12)*e^8 + x - 12)*e^(-2*x/(e^8 + 1)) + 2*x)/(e^8 + 1) + 2*x/(e^8 + 1))

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giac [B]  time = 0.54, size = 212, normalized size = 10.60 $$\begin{array}{c}\frac{(e^{(-\frac{2x{e}^8+x{e}^{(-\frac{2(x-4e^8-4)}{e^8+1}+8)}+x{e}^{(-\frac{2(x-4e^8-4)}{e^8+1})}-12e^{(-\frac{2(x-4e^8-4)}{e^8+1}+8)}-12e^{(-\frac{2(x-4e^8-4)}{e^8+1})}}{e^{16}+e^8}+16)}+e^{(-\frac{2x{e}^8+x{e}^{(-\frac{2(x-4e^8-4)}{e^8+1}+8)}+x{e}^{(-\frac{2(x-4e^8-4)}{e^8+1})}-12e^{(-\frac{2(x-4e^8-4)}{e^8+1}+8)}-12e^{(-\frac{2(x-4e^8-4)}{e^8+1})}}{e^{16}+e^8}+8)})e^{\left(\frac{2(x-4e^8-4)}{e^8+1}\right)}}{e^8+1}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(2)^4+2*x-25)*exp((12-x)/exp(2*x/(exp(2)^4+1)))/(exp(2)^4+1)/exp(2*x/(exp(2)^4+1)),x, algorithm
="giac")

[Out]

(e^(-(2*x*e^8 + x*e^(-2*(x - 4*e^8 - 4)/(e^8 + 1) + 8) + x*e^(-2*(x - 4*e^8 - 4)/(e^8 + 1)) - 12*e^(-2*(x - 4*
e^8 - 4)/(e^8 + 1) + 8) - 12*e^(-2*(x - 4*e^8 - 4)/(e^8 + 1)))/(e^16 + e^8) + 16) + e^(-(2*x*e^8 + x*e^(-2*(x
- 4*e^8 - 4)/(e^8 + 1) + 8) + x*e^(-2*(x - 4*e^8 - 4)/(e^8 + 1)) - 12*e^(-2*(x - 4*e^8 - 4)/(e^8 + 1) + 8) - 1
2*e^(-2*(x - 4*e^8 - 4)/(e^8 + 1)))/(e^16 + e^8) + 8))*e^(2*(x - 4*e^8 - 4)/(e^8 + 1))/(e^8 + 1)

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maple [A]  time = 0.10, size = 17, normalized size = 0.85

method	result	size
risch	${\mathrm{e}}^{-(x-12){\mathrm{e}}^{-\frac{2x}{{\mathrm{e}}^8+1}}}$	$17$
norman	${\mathrm{e}}^{(12-x){\mathrm{e}}^{-\frac{2x}{{\mathrm{e}}^8+1}}}$	$22$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-exp(2)^4+2*x-25)*exp((12-x)/exp(2*x/(exp(2)^4+1)))/(exp(2)^4+1)/exp(2*x/(exp(2)^4+1)),x,method=_RETURNVE
RBOSE)

[Out]

exp(-(x-12)*exp(-2*x/(exp(8)+1)))

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maxima [A]  time = 0.65, size = 27, normalized size = 1.35 $$\begin{array}{c}{e}^{(-x{e}^{(-\frac{2x}{e^8+1})}+12e^{(-\frac{2x}{e^8+1})})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(2)^4+2*x-25)*exp((12-x)/exp(2*x/(exp(2)^4+1)))/(exp(2)^4+1)/exp(2*x/(exp(2)^4+1)),x, algorithm
="maxima")

[Out]

e^(-x*e^(-2*x/(e^8 + 1)) + 12*e^(-2*x/(e^8 + 1)))

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mupad [B]  time = 0.23, size = 28, normalized size = 1.40 $$\begin{array}{c}{\mathrm{e}}^{12{\mathrm{e}}^{-\frac{2x}{{\mathrm{e}}^8+1}}}{\mathrm{e}}^{-x{\mathrm{e}}^{-\frac{2x}{{\mathrm{e}}^8+1}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(2*x)/(exp(8) + 1))*exp(-exp(-(2*x)/(exp(8) + 1))*(x - 12))*(exp(8) - 2*x + 25))/(exp(8) + 1),x)

[Out]

exp(12*exp(-(2*x)/(exp(8) + 1)))*exp(-x*exp(-(2*x)/(exp(8) + 1)))

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sympy [A]  time = 0.26, size = 14, normalized size = 0.70 $$\begin{array}{c}{e}^{(12-x)e^{-\frac{2x}{1+e^8}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-exp(2)**4+2*x-25)*exp((12-x)/exp(2*x/(exp(2)**4+1)))/(exp(2)**4+1)/exp(2*x/(exp(2)**4+1)),x)

[Out]

exp((12 - x)*exp(-2*x/(1 + exp(8))))

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