If `int(dx)/(x^(1/3)+2)=g(x)+c` then `g(-1)-(1)/(2)`

If int(dx)/(x^(2)+ax+1)=f(g(x))+c, then

f and g be two positive real valued functions defined on [-1,1] such that f(-x)=(1)/(f(x)) and g is an even function with int_(-1)^(1)g(x)dx = 1 then I = int_(-1)^(1)f(x)g(x)dx satisfies

int f(x)dx=g(x)+c then int f^(-1)(x)dxis

Let f(x)=2x+1 and g(x)=int(f(x))/(x^(2)(x+1)^(2))dx . If 6g(2)+1=0 then g(-(1)/(2)) is equal to

If int(dx)/(x+x^(2011))=f(x)+C_(1) and int(x^(2009))/(1+x^(2010))dx=g(x)+C_(2) (where C_(1) and C_(2) are constants of integration).Let h(x)=f(x)+g(x) .If h(1)=0 then h(e) is equal to

If int(dx)/(x+x^(2011))=f(x)+C_(1) and int(x^(2009))/(1+x^(2010))dx=g(x)+C_(2) where C_(1) and C_(2) are constants of integration.Let h(x)=f(x)+g(x) . If h(1)=0 then h(e) is equal to