Derivative of a definite integral

[CalculusHelp1]

Homework Statement

The problem:

Find the derivative of

x² multiplied by the integral of dt/(t-2t²) from x to -x²+2x

i.e, the function is x^2 times integral of [1/(t-2t^2)]dt from a to b with a being x and b being -x^2+2x

Homework Equations

Derivative and integral definitions

The Attempt at a Solution

Without the x^2 in front of the integral I think I can handle this question. I believe it would just be the function inside of the integral [1/(x-2x^x)] multiplied by -2x +2 (which is the derivative of the upper limit). Am I on the right track? If so, how do you handle the multiplier in front of the integral?

 

[vela]

Hint: The fundamental theorem of calculus tells you that

$$\int_x^{-x^2+2x} \frac{dt}{t-2t^2} = F(-x^2+2x)-F(x)$$

where F'(t) = 1/(t-2t²).