Question

Evaluate:`int(tansqrtx)/sqrtxdx`

Answer 1

`"I" =int(tansqrtx)/sqrtxdx`

Put √x = t

`therefore (dx)/(2sqrtx)="dt"`

`therefore (dx)/(sqrtx)="2dt"`

∴ I = ∫ tan t 2dt

= 2log |sec t| + C

= 2log |sec √x| + C