Ask
your own question, for FREE!
Mathematics
38 Online
Find integral sign 10/(4+x^2) dx using the substitution x=2 tan theta. (Give your answer in terms of x.)
Still Need Help?
Join the QuestionCove community and study together with friends!
\[\int\limits 10/(4+x^2) dx = 10*\int\limits1/(4+x^2) dx\] Let \[x=2*\tan \theta\]and \[dx = 2*\sec^2\theta d\theta\] Then, \[10*\int\limits 1/(4+4*\tan^2 \theta)*2*\sec^2 \theta d\theta\] Factor out a 4 in the denominator:\[10*\int\limits 1/(4*(1+\tan^2\theta))*2*\sec^2\theta d\theta\] Use the trig identity \[1+\tan^2\theta=\sec^2\theta\]Then, \[10*\int\limits (2*\sec^2\theta)/(4*\sec^2\theta) d\theta\]and \[10*\int\limits 1/2 d\theta=5*\int d\theta=5\theta\] Now, solve x=2*tan(theta) for theta and get \[\theta=\tan^-1(x/2)\]Thus, the answer is \[5*\tan^-1(x/2) + c\]
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
uknownprttyfacekayla:
I just wanna say happy birthday to my eldest brother @joshsimmoms your the best b
here4s:
(A freestyle written by me) shoutout to Nainoah for sayin I was good -repost cus I don't know how to spell.
here4s:
(A freestyle written by me) shoutout to Nainoah for saying I was good Yesterday was April fools, I was the only fool, I thought everything you said was true
LunaBechtold:
Why am i not perfect Is it the way i act? They way i need attention? The way i speak? No.
scarlettmiris:
Poem I wrote -Tattoo I look for you on an empty street Waiting in anticipation, f
14 minutes ago
8 Replies
1 Medal
5 hours ago
0 Replies
0 Medals
5 hours ago
0 Replies
0 Medals
7 hours ago
5 Replies
0 Medals
5 hours ago
6 Replies
3 Medals