Ask
your own question, for FREE!
Mathematics
33 Online
OpenStudy (anonymous):
integral of 1/ ((x) * sqrt(x+1))) dx
Still Need Help?
Join the QuestionCove community and study together with friends!
OpenStudy (anonymous):
this is a very difficult integral so if someone can help me I would appreciate it
OpenStudy (mathmagician):
The answer is \[\int\limits_{?}^{}1/(x \sqrt{1+x})dx=-2*arctanh(\sqrt{x+1)}\]
OpenStudy (anonymous):
Ya i figure that out, helllla hard to do though!
OpenStudy (anonymous):
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.
OpenStudy (anonymous):
i did u= x+1
Still Need Help?
Join the QuestionCove community and study together with friends!
OpenStudy (anonymous):
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
Late:
Roses in a vase, Sitting with a grin, Thorns are poking out, But they still let in.
27 minutes ago
2 Replies
1 Medal
Countless7Echos:
TW: distrubing images, scars, and slight blood)) so umm.. Ik I showed the finished product already but I started crashing out cause the shading was bugging
25 minutes ago
6 Replies
0 Medals
SnowyBreaks:
You know, Its funny how people wanna hurt you so bad, just because they have problems in there own life.
25 minutes ago
7 Replies
2 Medals
CHRiiis:
In sunny days and rainy nights You stand with me my heart's delight. With laughter shared and secrets told Our friendship shines a bond of gold.
5 hours ago
0 Replies
0 Medals
Bounty:
As We awaited the moon to take a late-night drive Wondering how we survived as yo
21 minutes ago
4 Replies
3 Medals
Late:
The moonlight bathes the night, Casting dreams in soft white, Whispers dance on the breeze, Carrying secrets with ease.
6 hours ago
8 Replies
1 Medal
MaxTon:
I started writing this song to help with addiction and murder, but I'm stuck on it rn, lemme know if you think it's worth finishing.
6 hours ago
1 Reply
1 Medal
Cloud4444:
When we become friends I will stand up for you, I will listen to you and we can t
9 hours ago
6 Replies
2 Medals