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What is int (dx)/(a^(2) sin^(2)x + b^(2)...

What is `int (dx)/(a^(2) sin^(2)x + b^(2) cos^(2)x)` equal to ?

A

`c + (1)/(ab) tan^(-1) ((a tanx)/(b))`

B

`c - (1)/(ab) tan^(-1) ((b tanx)/(a))`

C

`c + (1)/(ab) tan^(-1) ((b tan x)/(a))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I = (1)/(a^(2)) int (sec^(2)x)/(tan^(2) x + ((b)/(a))^(2))`
`= (1)/(a^(2)) xx (a)/(b) tan^(-1) ((a tan x)/(b)) + c`
`= c + (1)/(ab) tan^(-1) ((a tan x)/(b))`
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