Let `f(x)=|(cos x,e^(x^2) , 2x cos^2x/2),(x^2, sec x, sinx+x^3),(1,2,x+tan x)|` then the value of `int_(-pi/2)^(pi/2)(x^2+1)(f(x)+f''(x))dx `

If f(x) = |{:(cos x ,e^(x^(2)),2xcos^(2)((x)/(2))),(x^(2),secx,sinx+x),(1,2,x+tanx):}| the value of f_(-pi//2)^(pi//2)(x^(2)+1) [f(x)+f''(x)]dx is

If f(x) = |{:(cos x ,e^(x^(2)),2xcos^(2)((x)/(2))),(x^(2),secx,sinx+x),(1,2,x+tanx):}| the value of f_(-pi//2)^(pi//2)(x^(2)+1) [f(x)+f''(x)]dx is

If f(x) = |(x,cos x,e^(x^(2))),(sin x,x^(2),sec x),(tan x,1,2)| , then the value of int_(-pi//2)^(pi//2) f(x) dx is equal to

if f(x)=det[[x,cos x,e^(x^(2))sin x,x^(2),sec xsin x,x^(2),sec xtan x,1,2]] then the value of int_((-pi)/(2))^((pi)/(2))f(x)dx is equal to

if f(x)=|[x,cosx,e^(x^2)],[sinx,x^2,secx],[tanx,1,2]| then the value of int_((-pi)/2)^(pi/2) f(x)dx is equal to

Let f(x) = |{:(2cos ^(2) x,,sin 2x,,-sin x),(sin 2x,,2 sin^(2)x,,cos x),(sin x,,-cos x,,0):}| .then the value of int_(0)^(pi//2) [ f(x) +f'(x) ] dx " is "

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .