What is f(x) = int tanx-secx dx if f(pi/4)=-1 ?

1 Answer
Jan 7, 2018

f(x)=-ln|cosx|-ln|secx+tanx|-ln(sqrt2/(sqrt2+1))-1

Explanation:

As inttanxdx=-ln|cosx| and intsecxdx=ln|secx+tanx|

f(x)=int(tanx-secx)dx

= -ln|cosx|-ln|secx+tanx|+c

Hence f(pi/4)=-ln|1/sqrt2|-ln|sqrt2+1|+c=-1

or ln(sqrt2)-ln(sqrt2+1)+c=-1

or ln(sqrt2/(sqrt2+1))+c=-1

or c=-ln(sqrt2/(sqrt2+1)))-1

and f(x)=int(tanx-secx)dx

= -ln|cosx|-ln|secx+tanx|-ln(sqrt2/(sqrt2+1))-1