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In this paper, we obtain analytical solution of an unsolved integral$\textbf{R}_{C}(m,n)$ of Srinivasa Ramanujan [$\textit{Mess. Math}$., XLIV,75-86, 1915], using hypergeometric approach, Mellin transforms, InfiniteFourier cosine transforms, Infinite series decomposition identity and somealgebraic properties of Pochhammer's symbol. Also we have given somegeneralizations of the Ramanujan's integral $\textbf{R}_{C}(m,n)$ in the formof integrals $\textbf{I}^{*}_{C}(\upsilon,b,c,\lambda,y), \textbf{J}_C(\upsilon,b,c,\lambda,y), \textbf{K}_{C} (\upsilon,b,c, \lambda,y),\textbf{I}_{C}(\upsilon,b,\lambda,y)$ and solved it in terms of ordinaryhypergeometric functions ${}_2 F_3$, with suitable convergence conditions.Moreover as applications of Ramanujan's integral $\textbf{R}_{C}(m,n)$, the newnine infinite summation formulas associated with hypergeometric functions${}_{0}F_{1}$, ${}_{1}F_{2}$ and ${}_{2}F_{3}$ are obtained.

Generalizations of Ramanujan integral associated with infinite Fourier cosine transforms in terms of hypergeometric functions and its applications