Folosim formula lui King:
[tex] \int_a^b f(x)\, dx = \int_a^b f(a+b-x) \,dx[/tex]
∫₀¹⁰²⁴ ln(2017-x)/(ln(1505²-(512-x)²) dx =
= ∫₀¹⁰²⁴ ln(2017-(0+1024-x))/(ln(1505²-(512-(0+1024-x))²) dx =
=∫₀¹⁰²⁴ ln(993+x)/(ln(1505²-(-512+x)²) dx =
= ∫₀¹⁰²⁴ ln(993+x)/(ln(1505²-(512-x)²)dx
=> 2I = ∫₀¹⁰²⁴ ( ln(2017-x)/(ln(1505²-(512-x)²) + ln(993+x)/(ln(1505²-(512-x)²)) dx
=> 2I = ∫₀¹⁰²⁴ (ln((2017-x)(993+x))/(ln((1505-(512-x))(1505+(512-x)))dx =
= ∫₀¹⁰²⁴ ln((2017-x)(993+x))/(ln((2017-x)(993+x)))dx= ∫₀¹⁰²⁴ 1 dx
=> 2I = x | ₀¹⁰²⁴ => 2I = 1024 => I = 1024/2 => I = 512
