Find the general antiderivative of the function below. Use C for the constant of integration (please correct my logic)

Question

This is one of my last few problems, and I am just not getting this right.

It says "Find the general antiderivative of the function below. Use C for the constant of integration"

then it gives

f(t)=(t⁴-1)/t

I tried to integrate and I got ((t⁵/5)-t)/(t²/2)

Please help me figure this one out?

Thank you. 

Answer 1

f(t)=(t⁴-1)/t = t³ - 1/t 

 

Antiderivative is F= (¼)t⁴  - ln |x| + C.

 

Check by doing F'(t); you should get = f(t).

Answer 2

Hi Phil,

 

We have f(t) = (t⁴ - 1)/t

 

We can distribute 1/t to each term and write

 

f(t) = t⁴/t - 1/t = t³ - t^-1

 

F(t) = ∫(t³ - t^-1)dt

       = ∫t³dt - ∫t^-1dt

       = (1/4)t⁴ - ln|t| + C