It is well known that some definite integrals such as $$\int_{0}^{\pi} \frac{dx}{a+\cos{x}}$$ $$\int_{0}^{\infty} \frac{\sin{x}}{x}dx$$ are solved by using complex analysis techniques. (It uses residue theorem.)

But some of them are proved by only substitution like Harish Chandra Rajpoot answer. $$\int_{0}^{\pi} \log(\sin{x}) dx =-\pi\log{2}$$ (See definite integral without using complex line integral)

Are there any definite integral problems those cannot be soloved without complex line integral tecniques?