Answer to Question #174624 in Calculus for Phyroe

Question

Evaluate the integral of e^x + e^(-x) dx/(e^x - e^(-x))

Answer 1

GIVEN:

$\int{e^x+ e^{-x}\over e^x- e^{-x}}dx$

LET,

$e^x-e^{-x}$ =t

Therefore,

Differentiating this we get,

$(e^x+ e^{-x})$ dx=dt

Then,

$\int{dt\over t}$ We get,

$=ln(t)\\=ln(e^x-e^{-x})+c$ ....answer