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Prove the above following integral
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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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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