In this chapter, we obtain analytical expressions of infinite Fourier sine and cosine transform-based Ramanujan integrals, RS,Cmn=∫0∞xm−1+exp2πxsincosπnxdx, in an infinite series of hypergeometric functions 2F3⋅, using the hypergeometric technique. Also, we have given some generalizations of the Ramanujan’s integrals RS,Cmn in the form of integrals denoted by IS,C∗υbcλy,JS,Cυbcλy,KS,Cυbcλy and IS,Cυbλy. These generalized definite integrals are expressed in terms of ordinary hypergeometric functions 2F3⋅, with suitable convergence conditions. Moreover, as applications of Ramanujan’s integrals RS,Cmn, some closed form of infinite summation formulas involving hypergeometric functions 1F2, 2F3⋅, and 0F1 are derived.