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Prove the above following integral

 


 


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Prove the above following integral

Grade:12

2 Answers

Ramesh V
70 Points
12 years ago

put t =ex/(x2+1)1/2

     dt = 1/(x2+1)*(ex.(x2+1)1/2 - ex.x/(x2+1)1/2)

         = ex(x2-x+1)/(x2+1)

I = integral of ( t.dt)

  =t2/2 + C

  = e2x/2.(x2+1)   + C

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vikas askiitian expert
509 Points
11 years ago

integral of e^x.(x^2-x+1)/(x^2+1)3/2

 

above expression can be rewritten as e^x.([x^2+1]/[x^2+1]^3/2 + [-x/(x^2+1)3/2])

 

integral of e^x(fx + dfx/dx) =e^x.fx +c

 

  so ans is e^x.1/(x^2+1)^1/2 

 

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