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  • Integrate: ( x^2 +sin^2 x) sec^2 x / (1+x^2)

Integrate: ( x^2 +sin^2 x) sec^2 x / (1+x^2)

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Solution: 

         I=int frac(x^2+sin^2x)sec^2x1+x^2dx          

    ecause       sin^2x+cos^2x=1     and     sec^2x=frac1cos^2x

Now ,         \ \ I=int frac(x^2+sin^2x)(1+x^2)cos^2xdx

                \ \ I=int frac(x^2+1-cos^2x)(1+x^2)cos^2xdx\ \ I=int frac(x^2+1)(x^2+1)cos^2xdx -int fraccos^2x(x^2+1)cos^2xdx \ \ I=int sec^2x dx-int frac11+x^2dx\ \ I= an x- an^-1x+c.

          

Posted by

Deependra Verma

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