Ask
your own question, for FREE!
Mathematics
18 Online
Integral of 1/(u^3 + 3u) du, without using partial fractions? Many thanks!
Still Need Help?
Join the QuestionCove community and study together with friends!
This can be done by some none obvious algebra manipulation: integral [ 1/(u^3 + 3u) du ] = 1/3 * integral [ 3/(u^3 + 3u) du ] =1/3 * integral [ 3/{u*(u^2+3) du ] =1/3 * integral [ {3+u^2-u^2} / {u*(u^2+3)} du ] =1/3*integral [ {3+u^2} / {u*(u^2+3)} du ] - 1/3*integral [ {u^2} / {u*(u^2+3)} du ] =1/3*integral [ 1/u du ] - 1/3*integral [ u/{u^2+3} du] let u^2+3 = t => dt = 1/(2*u) du =1/3*ln(u) - 1/3 * 1/2 * integral (1/t dt) =1/3*ln(u) - 1/3*1/2*ln(t) =1/3*ln(u) - 1/3*ln(sqrt(t)) =1/3*ln( u / sqrt(t) ) =1/3*ln( u / sqrt(u^2+3) ) + C
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
xXAikoXx:
I need help. Does anybody know any tips on how to relax and not fear? I'm struggling to do that right now.
jinxthelovely:
does anybody have any tips on how to do geomotry?? im struggling
SnowyBreaks:
What's the best and safest way to catch a wild squirrel in your house-?
BloodyMoney:
https://open.spotify.com/track/40QrLHWdsxyXLAdjJG4Rxs?si=937451cbf1dc46d1 This so
bigbaddiedaddy:
hey question cove, I got a very debatable subject here and hoping to get lots of opinions.
Twaylor:
Question: Hypotheticaly if you went the frame rate of the universe (plank time), and turned that into " 1 plank time to 1 meter ", could you essentially tel
27 minutes ago
4 Replies
1 Medal
7 hours ago
3 Replies
1 Medal
1 day ago
3 Replies
1 Medal
1 day ago
1 Reply
0 Medals
1 day ago
19 Replies
2 Medals
2 days ago
18 Replies
2 Medals