x/1+ x - NCERT Class XII Mathematics Chapter - - Solutions

NCERT Class XII Mathematics Chapter - - Solutions

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

Question : 70 of 271

Marks: +1, -0

\frac{\cos x}{1+\cos x}

Solution:

Let

I=\int\frac{\cos x}{1+\cos x}dx

=\int\frac{(1+\cos x)-1}{1+\cos x}dx

=\int 1dx-\int\frac{1}{1+\cos x}dx

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

=\int dx-\frac{1}{2}\int\sec^2\frac{x}{2}dx

=x-\frac{1}{2}\cdot\frac{\tan\frac{x}{2}}{\frac{1}{2}}+C

=x-\tan\frac{x}{2}+C

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