D / DX (∫ e ^ √ TDT), that is, how to calculate the definite integral between X ^ 2 and x ^ 3

D / DX (∫ e ^ √ TDT), that is, how to calculate the definite integral between X ^ 2 and x ^ 3

Let ∫ e ^ √ TDT = f (T), then the definite integral between X ^ 2 and x ^ 3 = f (x ^ 3) - f (x ^ 2)
Then, take the derivative of x = f '(x ^ 3) * 3x ^ 2-F' (x ^ 2) * 2x = 3x ^ 2 * e ^ √ x ^ 3-2x * e ^ √ x ^ 2 = 3x ^ 2 * e ^ x √ x-2x * e ^ X