Some typical integrals are innovated and in course of evaluating these integrals two unusual integrals∫▒dx/(1+x^4 ) and ∫▒dx/(x√(1+x^4 )) are encountered. A number of such integrals are evaluated by parts. In some integrals the integrands are inverse circular functions. In some integrals the integrands are Logarithmic functions. The most of these integrals are converted into the foregoing types of integrals on simplification and elaborations to underscore the final results .Also evaluated are the integrals: ∫▒dx/(x^4+x^2+1),∫▒(x^2 dx)/(x^4+x^2+1), ∫▒(x^2 dx)/(x^4-x^2+1), ∫▒dx/(〖(2+x^2)〗^2+5), ∫▒log (x^4+4x^2+9)dx,∫▒log(x^4+4x^2+9)/x^2 dx ,etc.