If f(x)=1cos2x1+tanx then its anti-derivative F(x) ,F(0) = 4 is
1+tanx+4
23(1+tanx)3/2
2(1+tanx+1)
none of these
F(x)=∫dxcos2x1+tanx+C=∫11+tdt+C(t=tanx)=2(1+t)+C=21+tanx+C
Since 4=F(0)=2+C⇒C=2 Hence
F(x)=2(1+tanx+1)