integration - Solving an integral in R gives error "The integral is probably divergent" -

i trying solve integral in r. however, getting error when trying solve integral.

the equation trying solve follows:

$$ c_m = \frac{{abs{x}}e^{2x}}{\pi^{1/2}}\int_0^t t^{-3/2}e^{-x^2/t-t}dt $$ 

the code using follows:

a <- seq(from=-10, by=0.5,length=100)  ## create function compute integration cfun <- function(xx, upper){   integrand <- function(x)x^(-1.5)*exp((-xx^2/x)-x)   integrated <- integrate(integrand, lower=0, upper=upper)$value   (final <- abs(xx)*pi^(-0.5)*exp(2*xx)*integrated) }   b<- sapply(a, cfun, upper=1) 

the error getting follows:

error in integrate(integrand, lower = 0, upper = upper) :    integral divergent 

does mean cannot solve integral ?

any possible ways fix problem highly appreciated.

thanks.

you wrap call cfun in try statement

# note using `lapply` errors don't coerce result character b <- lapply(a, function(x,...) try(cfun(x, ...), silent = true), upper = 1) 

if wanted replace errors na values , print warning integration threw error

cfun <- function(xx, upper){   integrand <- function(x)x^(-1.5)*exp((-xx^2/x)-x)   int <- try(integrate(integrand, lower=0, upper=upper), silent = true)   if(inherits(int ,'try-error')){     warning(as.vector(int))     integrated <- na_real_   } else {     integrated <- int$value   }   (final <- abs(xx)*pi^(-0.5)*exp(2*xx)*integrated) } 

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edit (facepalm moment)

your error arises because function not defined when t=0 (you divide t within integrand).

cfun <- function(xx, upper){   integrand <- function(x)x^(-1.5)*exp((-xx^2/x)-x)   # deal xx=0   if(istrue(all.equal(xx, 0)){       warning('the integrand not defined @ xx = 0')       return(na_real_)   }   # deal other integration errors   int <- try(integrate(integrand, lower=0, upper=upper), silent = true)   if(inherits(int ,'try-error')){     warning(as.vector(int))     integrated <- na_real_   } else {     integrated <- int$value   }   (final <- abs(xx)*pi^(-0.5)*exp(2*xx)*integrated) }