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

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Solution:  We have ,

                I=int frac11+sin^2xdx=int frac12sin^2x+cos^2xdx

           \Rightarrow I=int fracsec^2x an^2x+(frac1sqrt2)^2dx ,

  Now ,   Put   an x=tRightarrow sec^2x dx=dt

          Rightarrow I=int frac1t^2+(frac1sqrt2)^2dt=frac1sqrt2 an^-1(sqrt2 an x)+c

Posted by

Deependra Verma

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