Hi !
there is a mishmash in your answer because the same symbol x is used for two different variables :
u=e^x
u=sinx
leading to e^x=sinx which is false.
Hi, I was wondering if you guys could check my work for indefinite integral of (e^x)(sqrt{1-e^2x)
Let u=e^x
The integral becomes:
integral of sqrt(1-u^2)
Then I do trigonometric substitution where I let u=sinx, and I get:
1/2sin^-1(x) + (x/2)*(1 - x^2)^1/2 + c.
However, the answer in my textbook is -1/3(1-e^(2x))^(3/2).
I was just wondering what I did wrong for the question.
If my complete process is wrong, what should I have done to solve the question?
Thanks in advance
You are just right put e^x=u that gives e^x dx = du
the question becomes integral of (1-u^2)^1/2 du and that is a standard for for which the integral is given by
(a^2-x^2)^1/2 = x/2 (a^2-x^2)^1/2 + 1/2 a^2 sin^-1 (x/a) + C
Thanks for the reply, I guess my initial answer was right then. Apparently the textbook has a different answer. It's -1/3(1-e^(2x))^(3/2).
I'm guessing the textbook used a different method then (integrate by part maybe? I didn't try it seemed way too complicated).
T.T wasted 30min on this question trying to figure out what I did wrong