`int_(-pi//2)^(pi//2) (x^(2)+log (pi+x)/(pi-x)) cos x dx` का मान ज्ञात कीजिए

Explanation

दिया है : `int_(-pi//2)^(pi//2) (x^(2)+"log" (pi+x)/(pi-x))cos x dx" "[ :' int_(-a)^(a) f(x) dx =0]`
`=int_(-pi//2)^(-pi//2) x^(2) cos dx +int_(-pi//2)^(pi//2) "log" (pi+x)/(pi-x) cos x dx`
`=2 int_(0)^(pi//2) x^(2) cos x dx+0" "[ :' int_(-a)^(a) f(x) dx=2 int_(0)^(a) f(x) dx]`
`=2[(x^(2) sin x)_(0)^(pi//2) - int_(0)^(pi//2) 2x sin x dx]`
`=2[pi^(2)/4 -0-2 {(-x cos x)_(0)^(pi//2)-int_(0)^(pi//2) 1.(-cos x) dx}]`
`=2 [pi^(2)/4-2xx0-2(sin x)_(0)^(pi//2)]`
`=pi^(2)/4-4`.