Question

How do you integrate `f(t)=(t^2+2)/(2t-7)` using the quotient rule?

Answer 1

There is no quotient rule for integration (only differentiation). Perform the implied division and integrate the terms of the quotient and the remainder.

Explanation:

Use either synthetic or long division to obtain the following:

`(t^2 + 2)/(2t - 7) = (1/2)t + 7/4 + 57/4(1)/(2t - 7)`

Integrate both sides of the equation:

`int(t^2 + 2)/(2t - 7)dt = (1/2)inttdt + 7/4intdt + 57/4int1/(2t - 7)dt`

`int(t^2 + 2)/(2t - 7)dt = (1/4)t^2 + 7/4t + 57/8ln(2t - 7) + C`