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Evaluate: int0^(pi//2)1/((a^2cos^2x+b^2s...

Evaluate: `int_0^(pi//2)1/((a^2cos^2x+b^2sin^2x)dx`

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`int_(0)^(pi//2) (dx)/(a^(2) cos^(2) x+b^(2) sin^(2) x)`
`=int_(0)^(pi//2) (sec^(2) x)/(a^(2) +b^(2) +tan^(2)x ) dx`
Divide munerator and denominator by `cos^(2) x`.
`int_(0)^(oo) (dt)/(b(a^(2)+t^(2))) " " "Let " b tan x=t`
`At x=0 t=0 " "rArr "b sec^(2) x dx =t`
`At = (pi)/(2) , t = oo " "rArr " " sec^(2) x dx =)(dt)/(b)`
`=1/b.1/a [tan ^(-1) .(t)/(a)]_(0)^(oo)`
`=1/(ab) [tan^(-1) oo tan^(-1) 0]`
`=1/(ab) .(pi)/(2)=(pi)/(2ab).`
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