Question

∫ dt/((e^​t)+1)

How do work it out? The answer is: ln| [√(e^t+1) - 1] / [√(e^t+1) + 1] | . Thanks!

Answer 1

U-Substitution. Set u=e^t, then du=(e^t)dt=udt.

Answer 2

sorry, but what do you mean by udt?

Answer 3

Alright, let me be clearer.

∫dt/(e^t+1); problem
u=e^t; substitution
du=(e^t)dt; evaluating du
dt=du/e^t; evaluating dt
∫du/((e^t)(u+1)); sub in u=e^t
∫du/(u(u+1)); remember e^t=u
1=A(u+1)+Bu=Au+A+Bu=(A+B)u+A; partial fractions

Can you solve from here?

Answer 4

ah okay i understand now--thanks!