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integrate 1/((a^2)*(secx)^2+b^2)^0.5 with respect to x
I= dx/[ a2 sec2x + b2 ]
=sec2xdx/(sec2x)[ a2tan2x +a2 +b2 ] (multiplying sividing by sec2x1+
=sec2xdx/a(1+tan2x)[ tan2x + (a2 +b2 /a2) ]
put tanx =t
sec2xdx =dt
after substituting these
I=dt/a(1+t2)[t2 + (a2 +b2 /a2 ) ]
now integrate by using partial fraction & get ur ans
Check its derivative w.r.t to x...
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