GSL numerical integration for a function with no extra parameters

I have a problem where I need to numerically integrate a univariate function with multiple extra inputs other than the variable that's being integrated over. The integration is from zero to infinity.

I said without extra parameters because I already defined a class with the extra parameters being the private member variables. And then the operator functor is defined to accept just the integration variable (hence, univariate). With this class, I want to use the GSL numerical integration library (gsl/gsl_integration.h) to do the integration. Is there a way to define a member function for this integration inside the class using GSL?

#include <cmath>
#include <Rmath.h>
#include <algorithm>
#include <iterator>
#include <RcppArmadillo.h>
#include <progress.hpp>
#include <progress_bar.hpp>
#include <RcppGSL.h>
#include <gsl/gsl_integration.h>
#include <Rdefines.h>
// [[Rcpp::depends(RcppArmadillo, RcppProgress, RcppGSL)]]
using namespace arma;

class ObservedLik
{
private:
    const int& Tk;
    const arma::vec& resid;
    const arma::mat& ZEREZ_S;
    const double& nu;
    const double& maxll;
public:
    ObservedLik(const int& Tk_,
                const arma::vec& resid_,
                const arma::mat& ZEREZ_S_,
                const double& nu_,
                const double& maxll_) : Tk(Tk_), resid(resid_), ZEREZ_S(ZEREZ_S_), nu(nu_), maxll(maxll_) {}

    double operator()(const double& lam) const {
        double loglik = -M_LN_SQRT_2PI * static_cast<double>(Tk) + (0.5 * nu - 1.0) * lam - 0.5 * nu * lam + 0.5 * nu * (std::log(nu) - M_LN2) - R::lgammafn(0.5 * nu);
        double logdet_val;
        double logdet_sign;
        log_det(logdet_val, logdet_sign, ZEREZ_S);
        loglik -= 0.5 * (logdet_val + arma::accu(resid % arma::solve(ZEREZ_S, resid)));
        /***********************************
        subtract by maximum likelihood value
        for numerical stability
        ***********************************/
        return std::exp(loglik  - maxll);
    }

    double integrate() {
        /* do the integration here */
        gsl_integration_workspace * w
            = gsl_integration_workspace_alloc (1000);

        double result, error;

        gsl_function F; 
        F.function = &f; // make this the operator()
        F.params = &alpha; // I don't need this part

        gsl_integration_qagiu (&F, 0.0, 0, 1, 0, 1e-7, 1000,
                        w, &result, &error);
        return result;
    }
};