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Evaluate: int1/(a^2sin^2x+b^2cos^2x)\ dx...

Evaluate: `int1/(a^2sin^2x+b^2cos^2x)\ dx`

Text Solution

Verified by Experts

`int (1)/(a^(2) cos^(2) x+b^(2) sin^(2) x)dx`
`= int (sec^(2)x)/(a^(2)+b^(2) tan^(2) x)dx`
(Divide N' and D' by `cos^(2)`x)
Let `b tan x=t`
`=int(dt)/(b(a^(2)+t^(2)))" "rArr b sec^(2) x = (dt)/(dx)`
` =1/b.1/a tan^(-1) ((t)/(a))+c rArr sec^(2) x dx =(dt)/(b)`
`=(1)/(ab) tan^(-1) ((btanx)/(a)) +c.`
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