Tutorial Exercise Find the indefinite integral csc dx Step 1 Observe that 1 9 Multiply and divide the given integral csc dx by Therefore the integral becomes Step 2 1 Now g x g x 9 1 9 is the derivative of x Let g x x Step 3 csc 1 d x CSC dx Define f g x csc 1 such that f x CSC x Rewrite the given integral in terms of g x where F g x is the antiderivative of f g x csc dx 9 csc2 2 dx 9 1 The antiderivative of f x is 9 x 9 x dx 9 F g x C c x 65c x dx