Answer the questions that follow:

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

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

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

. (ii) Hence, compute

\displaystyle\int_0^{\pi/4}\frac{\sec^2x}{1+\tan x}\,dx

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

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