Question

Integrate.

Answer 1

\[\int\limits_{}^{} \frac{ dx }{ \sin ^4x + \cos ^4x }\]

Answer 2

have you tried t= tan x ?

Answer 3

\(\dfrac{\sec^4x}{1+\tan^4x} =\dfrac{(1+\tan^2x)\sec^2x}{1+\tan^4x} \)

Answer 4

Yeah, thank you very much.
We would get,\[\int\limits_{}^{} \frac{ 1+t^2 }{ 1+t^4 }dt\]
Which I know how to solve..

Answer 5

Solution

Answer 6

good!

Answer 7

@dpasingh don't just give out solutions :\

Answer 8

@dpasingh , the solution is given in your attachment is too lengthy. There is an easier way.

Answer 9

No...

Answer 10

This is the only way to integrate this problem.

Answer 11

After, you have the integration in 'u'. You can use the method as in this post.
http://openstudy.com/study#/updates/51d90bc9e4b015ed7421940a

Answer 12

@dpasingh