vikas askiitian expert
Last Activity: 14 Years ago
1) I=tan^-1secx+tanx)dx
secx+tanx=1+sinx/cosx
1+sinx=(sinx/2+cosx/2)^2
cosx=(cosx/2-sinx/2)(cosx/2+sinx/2)
I=tan^-1(sinx/2+cosx/2)/(cosx/2-sinx/2)dx
=tan^-(tanpi/4+x/2)dx
=(pi/4+x/2)dx =(pi/5)x + x^2/4 +k
2)I=(1+2tanx(tanx+secx)^1/2dx
=(1+tan^2x + tan^2x +2secxtanx)^1/2 dx
=( sec^2x +tan^2x +2tanxsecx)^1/2dx
= ((secx+tanx)^2 )^1/2dx
= ( secx+tanx )dx
=logsecx+tanx +logsecx +c
=log(secx+tanx)secx +c