Question

Can anyone explain how to find the integral of sec(x) or csc(x) with respect to x?

Answer 1

lalaly is the integral master today

Answer 2

\[\int\limits{secxdx}=\int\limits{secx \times \frac{secx+tanx}{secx+tanx}}dx\]\[=\int\limits{\frac{\sec^2 x+secxtanx}{secx+tanx}dx}\]
let u=secx+tanx
so the integration becomes \[\int\limits{\frac{du}{u}}=\ln|u|+C\]\[=\ln|secx+tanx|+C\]

Answer 3

same for csc(x) but u multiply by (cscx+cotx)/(cscx+cotx)

Answer 4

lol satelite:)

Answer 5

Holy crap, no wonder I couldn't figure it out on my own. Are there any other cases where we do this?

Answer 6

lalaly is correct

Answer 7

here is another version. apparently this was a big deal in the 17th century
http://en.wikipedia.org/wiki/Integral_of_the_secant_function