i am using the shortcut (dz/ dx) +(1-n)p(x)z = (1-n) q(x) as in the first photo . But , my ans is wrong ? which part of my working is wrong ? I have written the ANS GIVEN below my working
You've just integrated $\tan^n x$ as if it were $x^n$.
You should write $\tan^2 x \, \sec^4 x = (1+\tan^2 x)\tan^2 x \, \sec^2 x = \tan^2 x \, \sec^2 x + \tan^4 x \,\sec^2 x$ and then use $u = \tan x$ to integrate.