Ask
your own question, for FREE!
Mathematics
43 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
Yosad930:
okay another random question that even google itself isnt helping me with: why cant i zoom in and out anymore with the touchpad? yk how when you pinch your
AddieroniAndCheese:
Tips for studying for an AP exam in like a week? I barely know anything about chem T-T.
thereneelg:
Ok so. I need help. So for one of my songs in choir, The Power of Love. We have to hold one of the "Love"s for a long time.
Aniii:
What is the mean of the following set of numbers: 4, 8, 6, 5, 3? 5.0 5.2 6.0 7.0
gelphielvr:
(algebra 1) input data, revenue f(x) = initial amount(interest)^x question in the
Yosad930:
;-; exam is next tuesday, and i dont get a single thing (well maybe one or two) c
H1m:
What does tariffs mean and what are they exactly? I need an answer from someone that actually knows.
41 minutes ago
5 Replies
0 Medals
2 hours ago
3 Replies
1 Medal
43 minutes ago
12 Replies
1 Medal
11 hours ago
5 Replies
0 Medals
59 minutes ago
10 Replies
1 Medal
2 hours ago
15 Replies
0 Medals
10 hours ago
13 Replies
3 Medals