value of the integral 1 to 2 of [(3t^3)+(4t^2)-4t +1]/[(4t^5)-(4t^4)+(t^3) ?

Question

The first "..."is -4t and the second "..."is ^4 + t^3.

Answer 1

let's take the lower term
4t^5 - 4t^4 +t^3 = t^3 (4t^2 - 4t + 1)
so the integral can be divided to two integrals:
integral (3t^3 / t^3 (4t^2 - 4t + 1) ) +
Integral (t^3 (4t^2 - 4t + 1)/t^3 (4t^2 - 4t + 1))

= int ( 3 * (4t^2 - 4t + 1) ^-1) + int(1)

can you continue from here?

Answer 2

The integral is equal to:
-1/(2t^2) - 3/(2*(2t-1))

Evaluated at 2 and 1 and then subtracted you get:
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