What is the integral of cos(x)sec(s-pi) ?

The integral of cos(x)sec(s-pi) is cos(x)(ssec(s-pi)+ssec(s)-ln|tan(s)+sec(s)|)+C

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integral of cos(x)sec(s-pi)

\int cos (x) sec (s - π) d s

cos (x) (s sec (s - π) + s sec (s) - ln ∣ tan (s) + sec (s) ∣) + C

Solution steps

\int cos (x) sec (s - π) d s

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (x) \cdot \int sec (s - π) d s

Apply Integration By Parts

: s sec (s - π) - \int - s sec (s) tan (s) d s

= cos (x) (s sec (s - π) - \int - s sec (s) tan (s) d s)

\int - s sec (s) tan (s) d s = - s sec (s) + ln ∣ tan (s) + sec (s) ∣

= cos (x) (s sec (s - π) - (- s sec (s) + ln ∣ tan (s) + sec (s) ∣))

Simplify

= cos (x) (s sec (s - π) + s sec (s) - ln ∣ tan (s) + sec (s) ∣)

Add a constant to the solution

= cos (x) (s sec (s - π) + s sec (s) - ln ∣ tan (s) + sec (s) ∣) + C

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What is the integral of cos(x)sec(s-pi) ?
The integral of cos(x)sec(s-pi) is cos(x)(ssec(s-pi)+ssec(s)-ln|tan(s)+sec(s)|)+C