Integrate: 1 / cos^4 x sin^2 x

Answers (1)

Solution:

                I=int frac1cos^4xsin^2xdx\ \ Rightarrow hspace0.5cmI= int frac(sin^2x+cos^2x)^2cos^4xsin^2xdx\ \ Rightarrow hspace0.5cmI=int fracsin^4x+2sin^2xcos^2x+cos^4xcos^4xsin^2xdx\ \ Rightarrow hspace0.5cmI=int fracsin^2xcos^4xdx+2int frac1cos^2xdx+int frac1sin^2xdx      

              \ \ I=int frac	an^2xcos^2xdx+2	an x-cot x+c\ \ I=frac13	an^3x+2	an x-cot x+c

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