I have a function that I need to numerically integrate from $0$ to $+\infty$, given by:$$I = \int_0^{+\infty} \mathrm{d}x\,x\,T^2(x)f(x)$$where $T^2$ is an interpolated function that goes to $1$ at small $x$ and decays as $x^{-4}$ at large $x$.$f$ is an oscillating function with known zeroes:$$f(x) = j^2_1(\alpha x)\times\cos(\beta\log x)$$where $j_n$ is the spherical Bessel.Since I know the zeros $z_n$ of the integrand (thus having control on its oscillations), is it a good idea to split the integral in sub-integrals (from $z_n$ to $z_{n+1}$) and sum all the contributions?My idea was to change variables ($x = e^u$) and do the sub-integrals with SciPy's scipy.integrate.quad.
Numerical integral of oscillating function with known zeros
interpolation;quadrature;scipy;integration