What is f(x) = int tanx-secx dx if f(pi/4)=-1 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Shwetank Mauria 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 Answer link Related questions How do you find the constant of integration for intf'(x)dx if f(2)=1? What is a line integral? What is f(x) = int x^3-x if f(2)=4 ? What is f(x) = int x^2+x-3 if f(2)=3 ? What is f(x) = int xe^x if f(2)=3 ? What is f(x) = int x - 3 if f(2)=3 ? What is f(x) = int x^2 - 3x if f(2)=1 ? What is f(x) = int 1/x if f(2)=1 ? What is f(x) = int 1/(x+3) if f(2)=1 ? What is f(x) = int 1/(x^2+3) if f(2)=1 ? See all questions in Evaluating the Constant of Integration Impact of this question 1600 views around the world You can reuse this answer Creative Commons License