What is f(x) = int xsin4x+tanx dx if f(pi/4)=1 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer A. S. Adikesavan Feb 15, 2017 1/16(-4xcos(4x)+sin(4x)-16ln cosx-pi+15-8ln 2) Explanation: f(x)=int(-1/4xd(cos(4x))-1/((sinx)') d(cosx)) =-1/4(x cos(4x)-intcos(4x dx))-lncosx =-1/4xcos(4x)+1/16sin(4x)-logcosx +C As f(pi/4)=1, pi/16+1/16-ln(1/sqrt2)+C=1 So, C =-pi/16+15/16-1/2ln2. And so, f(x)=-1/4xcos(4x)+1/16sin(4x)-logcosx -pi/16+15/16-1/2ln2 =1/16(-4xcos(4x)+sin(4x)-16ln cosx-pi+15-8ln 2) 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 1475 views around the world You can reuse this answer Creative Commons License