Let `f(x)=1/(4-3cos^2x+5sin^2x)` and if its antiderivative `F(x)=(1/3) tan^-1(g(x))+C` then `g(x)` is equal to

Let f(x)=-2x^(2)+1 and g(x)=4x-3 then (gof)(-1) is equal to

If f(x) = 3x + 1 and g(x) = x^(2) - 1 , then (f + g) (x) is equal to

If f(x) = 3x + 1 and g(x) = x^(2) - 1 , then (f + g) (x) is equal to

If int (1)/(4-3 cos^(2) x+5sin^(2)x)dx=(1)/(3)tan^(-1)(f(x))+c ,then f(x)equals :

Let g(x) be an antiderivative for f(x). Then ln(1+(g(x))^(2)) is an antiderivative for

Let f(x)=|x-2|+|x-3|+|x+4| and g(x)=f(x+1) . Then g(x) is

Let f(x)=(9x)/(25)+c, c gt 0 . If the curve y=f^(-1)(x) passes through ((1)/(4), -(5)/(4)) and g(x) is the antiderivative of f^(-1)(x) such that g(0)=(5)/(2) , then the value of [g(1)] is, (where [.] represents the greatest integer function)