`f'''(t) = e^t + t^-4` Find `f`.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

`f'''(t)=e^t+t^(-4).`

Integrate this once:

`f''(t)=e^t+(-1/3)t^(-3)+C_1,`

twice:

`f'(t)=e^t+(-1/2)(-1/3)t^(-2)+C_1t+C_2,`

thrice:

`f(t)=e^t+(-1/1)(-1/2)(-1/3)t^(-1)+C_1t^2+C_2t+C_3= e^t-1/(6t)+C_1t^2+C_2t+C_3,`

where `C_1, ` `C_2,` `C_3` are any constants.