Evaluate the following integrals: `int_0^(pi//2)(tanx)/(1+m^2tan^2x)dx`

Explanation

`I=int_0^(pi//2)(tanx)/(1+m^2tan^2x)dx`

`I=int_0^(pi//2) ((sinx)/(cosx))/(1+m^2(sin^2x)/(cos^2x))dx`

`I=int_0^(pi//2) (sinxcosxdx)/(cos^2x+m^2sin^2x)`

`I=int_0^(pi//2) (sinxcosxdx)/((1-sin^2x)+m^2sin^2x)`

let `sin^2x=t`

`2sinxcosxdx=dt`



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