Antiderivative problem!!!?

Question

a) evaluate the antiderivative of f(t)= 1/(t^(2)+1)?

and...

b) evaluate the antiderivative of f(x)= x+ (4/sqrt(x))?

and...

c) find the antiderivative of f(x)= e^(t) + e^(5)?

Answer 1

1).arctan t + C.
2). x² /2 + 8√x + C.
3). x(e^t +e^5) + C.
In the last one we are integrating with respect to x,
so the integrand is constant with respect to x.

Answer 2

1) F(t) Arctan(t)+C
2) F(x) = x^2/2 +8*sqrt(x) +C
3)F(t) = e^t+(e^5 )* t +C (I think you mean e^t and f(t))