Integration problem

May 2010
4
0
Hello everyone,
I've been preparing for my cal exam and I got stuck on this problem:
Evaluate the infinite integral
\(\displaystyle \int \frac {\sec^4 x}{\sqrt(tan 2x)} dx\)
I would really appreciate if you give me a clue on how I should do it because I've been trying different trigonometric identities and other methods for quite some time with no results.
Thank you
 
Apr 2010
384
153
Canada
Hello everyone,
I've been preparing for my cal exam and I got stuck on this problem:
Evaluate the infinite integral
\(\displaystyle \int \frac {\sec^4 x}{\sqrt(tan 2x)} dx\)
I would really appreciate if you give me a clue on how I should do it because I've been trying different trigonometric identities and other methods for quite some time with no results.
Thank you
Midread the integrand...
 
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May 2010
4
0
I think you did not notice that it is a square root of tan(2x)... That is exactly what I was doing except that with square root it does not seem to lead anywhere. :(
 
Apr 2010
384
153
Canada
I think you did not notice that it is a square root of tan(2x)... That is exactly what I was doing except that with square root it does not seem to lead anywhere. :(
Edit- lag. You're right, give me a moment i'll try something
 
May 2010
4
0
Eh, well I found it in previous final exam. First year college calculus.. I know the answer but I wanted to know how to get it. Well thanks for a try, if I'll figure it out, I'll post it lol
 
Dec 2009
872
381
1111
Eh, well I found it in previous final exam. First year college calculus.. I know the answer but I wanted to know how to get it. Well thanks for a try, if I'll figure it out, I'll post it lol
Dear karfag,

Did your answer tally with the answer "Wolfram" suggested??
 
May 2010
4
0
The answer listed is

(tan(2x))^1/2 + 1/5 * (tan(2x))^5/2 + C

Sorry for not writing it the correct way, I'm not very familiar with the math tags syntax
 
Dec 2009
872
381
1111
The answer listed is

(tan(2x))^1/2 + 1/5 * (tan(2x))^5/2 + C

Sorry for not writing it the correct way, I'm not very familiar with the math tags syntax
Dear karfag,

Differentiate \(\displaystyle (tan(2x))^{1/2} + \frac{1}{5} (tan(2x))^{5/2}+C\) and you would obtain, \(\displaystyle \frac {\sec^{4} 2x}{\sqrt{tan 2x}}\). Hence the integration should be \(\displaystyle \int\frac {\sec^{4} 2x}{\sqrt{tan 2x}}\)
 
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