`intsec^2xcos^2 (2x) dx`

Explanation

Given,`∫ sec^2x cos^2 2x dx `

=` ∫ sec^2x (cos^2x – sin^2x)^2dx`


=`∫ sec^2x (cos^4x – 2cos^2xsin^2x +sin^4x)dx`

=`∫ (cos^2x – 2sin^2x +sin^4x/cos^2x)dx`

=`∫ cos^2x – 2sin^2x +((1-cos^2x)(1-cos^2x))/cos^2x)dx`

On multiplying `(1-cos^2x).(1-cos^2x) `equation reduces to,

=`int(cos^2x – 2sin^2x +sec^2x-2+cos^2x)dx`

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