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Evaluate: int1/(secx+cos e c\ x)\ dx...

Evaluate: `int1/(secx+cos e c\ x)\ dx`

Text Solution

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`int dx/ sec x + cosec x `
`= int (sin x cos x/ sin x + cos x) dx `
` = (1/2) int (2 sin x cos x/ sin x + cos x) dx`
`=int frac{(1+sin2x)-1}{sinx+cosx}dx`
`=1/2 int frac{(sinx+cosx)^2}{sinx+cosx}-1/2 int frac{1}{sinx+cosx}dx`
`=1/2(sinx+cosx)-1/(2 sqrt 2)log abs(tan(x/2 + pi/8))`
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