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प्रश्न
Evaluate the following integrals : `int cos^2x.dx`
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उत्तर
Recall the identity cos 2x = 2 cos2x – 1, which gives
`cos^2x = (1 + cos2x)/(2)`
Therefore, `int cos^2 x.dx`
= `(1)/(2)int (1 + cos 2x).dx`
= `(1)/(2)int dx + (1)/(2) int cos 2x .dx`
= `x/(2) + (1)/(4)sin 2x + C`.
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