So I used substituion, u = 1 + e-x, and -du = e-x dx
There it turns it into -∫(du/u), which equals -ln(1+e-x) + C
Then my partner told me the next step was ln(ex/(ex+1))
After that, he got it into x - ln (ex + 1) + C, which is the correct answer.
And I was confused on that part since it turned into something like a fraction. The part where it goes e x/ex+1 Can someone explain?
Another is ∫ex√(1-ex)dx
I did u = 1-ex, -du = ex dx
I plugged it in...
∫-du√(u) = -∫du(u1/2)
Not really sure if I'm doing this next step correctly... but I did that it = u1/2
Plugged in u: (1-ex)1/2
But the answer was: -2/3(1-ex)3/2 + C
I'm a bit confused now... since I'm integrating the 'e' along...
Can someone give a piece of advice or explain please?
Now that makes more sense!
I forgot to see that it had a negative exponent, which makes it goes down into the denominator, so the only way to convert the 1 to have them both at the same denominator is by having it ex as well!
While for the second one. I think I remember now! So basically after you integrate it, the exponent goes up by 1 and you would divide it by the exponent.
Thanks for helping me and reminding me of this stuff!