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Integrate: 1/1+cos^2x

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Solution: We have ,

                I=int frac11+cos^2xdx=int frac1sin^2x+2cos^2xdx

             I=int fracsec^2x an^2x+2dx    put ,  an x=tRightarrow sec^2x dx=dt

           I=int frac1t^2+2dt=frac1sqrt2 an^-1fractsqrt2+c

        Rightarrow             I= frac1sqrt2 an^-1(frac an xsqrt2)+c

Posted by

Deependra Verma

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