intg (e^2x+1)/e^x dx

Let t = e^x

==> dt = e^x dx = tdx ==> dx = dt/t

==> intg (e^2x+ 1)/e^x) dx = intg (t^2 + 1)/t * dt/t

= intg (t^2 + 1)/t^2 dt

= intg (1 + 1/t^2) dt

= intg (1+ t^-2) dt

...

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intg (e^2x+1)/e^x dx

Let t = e^x

==> dt = e^x dx = tdx ==> dx = dt/t

==> intg (e^2x+ 1)/e^x) dx = intg (t^2 + 1)/t * dt/t

= intg (t^2 + 1)/t^2 dt

= intg (1 + 1/t^2) dt

= intg (1+ t^-2) dt

= t - t^-1 + c

= e^x - e^-x + c