Question

what is the integration of sec2x.cosx

Answer 1

\[\sec^2x=\frac{1}{\cos^2x}\]
So \[\sec^2x*\cos x=\frac{1}{\cos^2x}*\cos x=\frac{\cos x}{\cos^2x}=\frac{1}{\cos x}=\sec x\]

Answer 2

Next step would be to integrate sec x
\[ \int \sec x dx \]
Ok using the table in the back of a calc book we see that the
\[ \int \sec x dx = \ln | \sec x + \tan x | +C\]