Problem

Answer the questions that follow: a. (i) Evaluate the indefinite integral

\displaystyle\int \dfrac{\sec^{2}x}{1+\tan x}\,dx

. b. (ii) Hence, compute

\displaystyle\int_{0}^{\pi/4} \dfrac{\sec^{2}x}{1+\tan x}\,dx

. c. (iii) Differentiate your result from part (i) to confirm that it is a correct antiderivative of

\dfrac{\sec^{2}x}{1+\tan x}