This integral cannot be performed analytically. Ony when the integral is taken from 0 to infinity can it be computed by squaring the integral and applying a change of variable (switching to polar coordinates).
if desired I could show how to do this.
Chat with our AI personalities
Euler's constant, e, has some basic rules when used in conjunction with logs. e raised to x?æln(y),?æby rule is equal to (e raised to ln(y) raised to x). e raised to ln (y) is equal to just y. Thus it becomes equal to y when x = 1 or 0.
e-2 = 1/e2 ≈ 0.1353
ln is the inverse of e. So the e and the ln cancel each other out and you are left with 2. eln2 = 2
The integral of esec(x) dx is not a function that may be expressed in terms of well-studied mathematical functions, elementary or nonelementary. In general, it must be evaluated by numerical methods.
e2ln2 + 2 = 22 + 2 = 4 + 2 = 6