Finding $\int \frac{dx}{(a^2\cos^2x+b^2\sin^2x)^2}$

Question

Find $\displaystyle\int \frac{dx}{(a^2\cos^2x+b^2\sin^2x)^2}$, where $a,b$ are constants.

I tried it some specific values of $a,b$ and tried many substitutions but it doesn't seem to work.

Just throw me a hint. Thanks.

Vidyanshu Mishra I received an invitation from you to join you in a chat; However, I cannot access that chat. So, I'll have to say "no thank you" for now — amWhy, Sep 14 '17 at 22:33
@amwhy actually I had something to discuss. But now I am a bit busy, let's leave it for sometime. At least till the end of my mid term exams. — Vidyanshu Mishra, Sep 15 '17 at 18:51

score 7 · Accepted Answer · answered Jul 23 '17 at 05:54

7

HINT:

$$\dfrac1{(a^2\cos^2x+b^2\sin^2x)^2}=\dfrac{\sec^4x}{\left(a^2+b^2\tan^2x\right)^2}$$

Write $b\tan x=a\tan y$

answered Jul 23 '17 at 05:54

lab bhattacharjee

1 Answers1