Method of steepest descent to approximate $\int_0^1\frac{\cos(\lambda x^3)}{\left(x-\frac{1}{2}\right)^2+(\frac{1}{20})^2}dx$

Question

Im trying to use the method of steepest decent to approximate the following integral: $$I(\lambda)=\int_0^1\dfrac{\cos(\lambda x^3)}{\left(x-\frac{1}{2}\right)^2+(\frac{1}{20})^2}dx$$ where $\lambda$ is a very large parameter. I know I can express the cosine as the real part of a complex exponential but I'm not sure how to proceed. Any help would be great. Thanks