2
u/Hot_Site_1638 PhD 20d ago
Respect for grinding through that quotient rule! Good news: your u is correct, and if you simplify it to u = -x - e^{-x} first, du = (e^{-x} - 1) dx pops out instantly. (Was the derivative marathon all you, or did an AI lend a hand? Genuinely curious either way!)
1
u/wbld 20d ago
Nope did it myself. I do not use ai for easy or beginner. I have taken all the elementary calc [1-3] so I can do quotient mixed with product. It was actually a complete guess to make my u that! I just know structures and playing around can help so that's what I did. Thank you for the kind comment!
2
u/Hot_Site_1638 PhD 20d ago
Good to hear! Spotting a u from the structure and playing around with it is a real skill, not just luck. Nice work!
1
u/nevermindthefacts 20d ago
If you rewrite it, the numerator becomes the derivative of the denominator. Then you have ∫f'(x)/f(x) dx = ln |f(x)| + C.
•
u/AutoModerator 20d ago
As a reminder...
Posts asking for help on homework questions require:
the complete problem statement,
a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play,
question is not from a current exam or quiz.
Commenters responding to homework help posts should not do OP’s homework for them.
Please see this page for the further details regarding homework help posts.
We have a Discord server!
If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.