(e^2x+1)/e^x dx integrate by substitution method

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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

                                           ...

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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

           

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