# Question:how integrate this kind of function?

## Question:how integrate this kind of function?

Maple

i use previous post link to derive again for weibull, the final integration seems can not be integrated,

any things need to notice?

Weibull
WeibullDist := (η/rho)*((x/rho)^(η-1))*exp(-((x/rho)^η));
WeibullDist := 1-summation((η/rho)*((x/rho)^(η-1))*exp(-((x/rho)^η)),x=0..k-1);
WeibullDist := int((η*z)*(((k-1)*z)^(η-1))*exp(-(((k-1)*z)^η)),z=0..1/rho);
WeibullDist := int((η*z)*(((k-1)*z)^(η-1))*exp(-(((k-1)*z)^η)),z=0..1/rho);
WeibullDensity := diff(WeibullDist, rho) assuming rho >= 0;
WeibullDensity := simplify(simplify(simplify(expand(convert(simplify(WeibullDensity, size), exp)), size)));
WeibullDensity := -eta*((k-1)/rho)^eta*exp(-((k-1)/rho)^eta)/(rho^2*(k-1));
WeibullDensity := subs(k=a,WeibullDensity);
WeibullDensity := subs(rho=x,WeibullDensity);
WeibullDensity := subs(eta=b,WeibullDensity);
WeibullDensity := -b*((a-1)/x)^b*exp(-((a-1)/x)^b)/(x^2*(a-1));
WeibullDensity := subs(a=t/v, WeibullDensity); # do not know why subs this
WeibullDensity := subs(x=g, WeibullDensity); # do not know why subs this
WeibullDensity := subs(b=1/v, WeibullDensity); # do not know why subs this
WeibullDensity := simplify(WeibullDensity);
tm := simplify(int(expand(1/(rho*sqrt(2*Pi*g))*exp(-((X-theta*g)^2)/(2*g*rho^2))*WeibullDensity),g=0..infinity));
a := int(exp(i*X*u)*tm, X = -infinity .. infinity);
madan := simplify(a, power) assuming rho > 0, theta > 0, v > 0;

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