Question

Evaluate the indefinite integral. ft-53 at 1250 + c 5 - + 2 - 125t + c 312 - 30t + 75 + 6 O r4 - 15+ 7512 - 125t + c

Answer 1

Given:

`∫(t-5)^3\text{ dt}`

Let's evaluate the integral:

`\begin{gathered} ∫(t-5)^3\text{ dt} \\ \\ =(1)/(4)(t-5)^4+c \\ \\ ^{} \end{gathered}`

Thus, we have:

`(1)/(4)(t^4-20t^3+150t^2-500t+625)+C`

Expand using distributive property:

`\begin{gathered} ((t^4)/(4)-(20t^3)/(4)+(150t^2)/(4)-(500t)/(4)+(625)/(4))+C \\ \\ \\ =(t^4)/(4)-5t^3+(75t^2)/(2)-125t+C \end{gathered}`

ANSWER:

`=(t^4)/(4)-5t^3+(75)/(2)t^2-125t+C`