How do you find the integral of 1cosx?
1 Answer
Apr 30, 2016
Explanation:
Note that
∫1cosxdx=∫secxdx
This is an important trigonometric identity:
∫secxdx=ln|secx+tanx|+C
If you want to know how to find
∫secxdx=∫secx(secx+tanx)secx+tanxdx=∫secxtanx+sec2xsecx+tanxdx
Now, use substitution:
u=secx+tanx ⇒ du=(secxtanx+sec2x)dx
Note that these are the fraction's numerator and denominator.
∫secxtanx+sec2xsecx+tanxdx=∫duu=ln|u|+C
Since
∫secxdx=ln|secx+tanx|+C