1/(x+a)(x+b) - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

..... Miscellaneous Exercise .....
Integrate the functions in Exercises 229 to 252.

Question : 239 of 271

Marks: +1, -0

\frac{1}{\cos(x+a)\cos(x+b)}

Solution:

Let

I=\int\frac{1}{\cos(x+a)\cos(x+b)}dx

=\frac{1}{\sin(a-b)}\int\frac{\sin[(x+a)-(x+b)]}{\cos(x+a)\cos(x+b)}dx

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

=\frac{1}{\sin(a-b)}\int[\tan(x+a)-\tan(x+b)]dx

=\frac{1}{\sin(a-b)}[\log\sec(x+a)-\log\sec(x+b)]+C

=\frac{1}{\sin(a-b)}\log\left|\frac{\sec(x+a)}{\sec(x+b)}\right|+C

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