Some typical integrals are innovated, and in the 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. Most of these integrals are converted to the foregoing integrals on simplification and elaborations to underscore the final results. Also evaluated are the integrals: ∫▒dx/((1+x^2)(1+x^4)), ∫▒(x^2 dx)/((1+x^2)(1+x^4)), ∫▒(x^3 dx)/((1+x^2)(1+x^4)),∫▒(x^4 dx)/((1+x^2 )(1+x^4 ),),∫▒(x^5 dx)/((1+x^2)(1+x^4)) ,∫▒(x^6 dx)/((1+x^2)(1+x^4)), and ∫▒(x^7 dx)/((1+x^2)(1+x^4)) .