Couldn't manage evaluating the integral: $\int_{i=1}^\infty cos(\theta ^{5})d\theta$
What I could figure out is that this integral doesn't converges absolutely because the function isn't bounded, but couldn't prove anything about convergence. Tried to use the substitution u=$\theta ^{3}$ but it gives nothing. Also tried to go with Taylor series but no Idea how to do that. Thanks!
I think I figured out the solution. because I needed only to check the convergence and haven't had to find the value of the integral, I can go this way:
substitute $u = y ^{5}$, then after arithmetic operations I will get to: $\frac{cos(x)}{x^{4/5}}$ then by dirichlet's theorem it converges but doesn't converge absolutely.