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# Prove the above following integral

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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Ramesh
IIT Kgp - 05 batch

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