Ask
your own question, for FREE!
Mathematics
27 Online
integral of 1/ ((x) * sqrt(x+1))) dx
Still Need Help?
Join the QuestionCove community and study together with friends!
this is a very difficult integral so if someone can help me I would appreciate it
The answer is \[\int\limits_{?}^{}1/(x \sqrt{1+x})dx=-2*arctanh(\sqrt{x+1)}\]
Ya i figure that out, helllla hard to do though!
It's not hard. Substitute \(u=\sqrt{x+1} \implies x=u^2-1 \implies dx=2udu\). That gives: \[\int\limits_{}^{}{dx \over x \sqrt{x+1}}=\int\limits {2u du \over (u^2-1)(u)}=\int\limits {2 \over u^2-1}=-2\int\limits {1 \over 1-u^2}=-2\tanh^{-1}u.\] Now, substitute back for x. You can also solve from the last step by using partial fractions.
i did u= x+1
Still Need Help?
Join the QuestionCove community and study together with friends!
That would work, but you will need another substitution, say \(z=\sqrt{u}\).
Can't find your answer?
Make a FREE account and ask your own questions, OR help others and earn volunteer hours!
Join our real-time social learning platform and learn together with your friends!
Join our real-time social learning platform and learn together with your friends!
Latest Questions
willowjade:
wrote this last night lmk what you think She just wanted to feel pretty. Sure she was called pretty by her parents.
Subshilava:
Does anybody have a college poster board layout I have my material but I cannot f
MaxTon:
I was feeling a bit down so I turned to writing how I felt down and made something out of it.
theydontknowmelly:
What's a good healthy diet for someone who's starting to workout daily ??
janaeDehon:
Which of the following lines best summarizes the story? A. The story details an African vacation from a long time ago, in which Sage's adventures are descri
Subshilava:
I have an issue my mom bought me a 3d cat mold from tj maxx and everytime I fill
ShikuniShigana:
Alright so. I need some art ideas, or Drawing design ideas for this Character im doing, He's Kinda like based off Vita Carnis+Shefki Shin+Death Angel(From Q
gelphielvr:
hello :] I have to make a model for my biology class for either topic "evolution"
51 seconds ago
12 Replies
3 Medals
1 day ago
0 Replies
0 Medals
15 hours ago
19 Replies
7 Medals
2 days ago
31 Replies
9 Medals
2 days ago
5 Replies
3 Medals
2 days ago
17 Replies
4 Medals
1 day ago
17 Replies
2 Medals
3 days ago
15 Replies
2 Medals