What is f(x) = int secx- cscx dx if f((5pi)/4) = 0 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Leland Adriano Alejandro Jan 18, 2016 f(x) = ln((sec x+tan x)/(csc x-cot x))+ ln((sqrt(2) +1)/(sqrt2-1)) Explanation: After integration f(x)=ln(sec x+tan x)-ln(csc x-cot x)+C f((5 pi)/4)=ln abs(sec((5 pi)/4)+tan ((5 pi)/4))-lnabs(csc ((5 pi)/4)-cot ((5 pi)/4))+C=0 ln abs(-sqrt2+1)-lnabs(-sqrt2-1)+C=0 C=ln abs(sqrt2+1)-lnabs(1-sqrt2) C=ln ((sqrt2+1)/(sqrt2-1)) 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 1330 views around the world You can reuse this answer Creative Commons License