Given,

Let tanx=t

Sec²x dx=dt

Now,

Now,

1≅ A(t-2)+B(2t+1)

Equating ‘t’ coeff: -

0=A+2B

A=-2B

Equating constant: -

1=-2A+B

1=-2(-2B) +B

_1=5B

B=

Now,