2x+2² x/² x - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.3
Find the integrals of the functions in Exercises 62 to 83.

Question : 79 of 271

Marks: +1, -0

\frac{\cos 2x+2\sin^2 x}{\cos^2 x}

Solution:

Let

I=\int\frac{\cos 2x+2\sin^2 x}{\cos^2 x}dx

=\int\frac{(\cos^2 x-\sin^2 x)+2\sin^2 x}{\cos^2 x}dx

=\int\frac{\cos^2 x+\sin^2 x}{\cos^2 x}dx

=\int\frac{1}{\cos^2 x}dx

=\int\sec^2 x\,dx=\tan x+C

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