A233382 Decimal expansion of the integral over dx/((1+x^2)(1+tan x)) in the limits 0 and Pi/2.

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Offset: 0

Author

R. J. Mathar, Dec 08 2013

Keywords

• cons
• less
• nonn

Examples

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Links

• juantheron, How to evaluate int_0^(pi/2) dx/(1+x^2)/(1+tan x), math.stackexchange, Apr 14 2013

Programs

Maple

Digits := 60 :
# Expand 1/(1+tan x) in a Taylor series around Pi/4 and exchange
# summation and integration.
for dd from 80 to 100 by 10 do
    taylor(1/(1+tan(z)),z=Pi/4,dd) ;
    gfun[seriestolist](%) ;
    c := evalf(%) ;
    x := 0.0 ;
    for i from 0 to nops(c)-1 do
        1/(1+zz^2)*op(i+1,c)*(zz-Pi/4)^i ;
        int(%,zz=0..Pi/2) ;
        x := x+evalf(%) ;
    end do:
    print(x) ;
end do:

Mathematica

RealDigits[ NIntegrate[ 1/((1+x^2)(1+Tan[x])),{x, 0, Pi/2}, WorkingPrecision -> 110], 10, 105][[1]] (* Robert G. Wilson v, Sep 29 2014 *)