Find f. f=______

Question

f'(t)= 8/1+t² , f(1)=0

Answer 1

f'(t) = 8 / (1 + t²)

f(t) = ∫f'(t)dt = 8∫[1 / (1 + t²)]dt = 8Arctant + C

Since f(1) = 0, we have 8Arctan1 + C = 0

8(π/4) + C = 0. So, C = -2π

f(t) = 8Arctant - 2π