Definite integral of F (2x + a) = Xe ^ X / b The upper limit of definite integral is y, and the lower limit is a + 2B. Find ∫ f (T) DT Calculus of Higher Education Press, edited by Liu Shutian, Chapter 1 of definite integral, 7.3, question 16

Definite integral of F (2x + a) = Xe ^ X / b The upper limit of definite integral is y, and the lower limit is a + 2B. Find ∫ f (T) DT Calculus of Higher Education Press, edited by Liu Shutian, Chapter 1 of definite integral, 7.3, question 16

f(x)=(x-a)/2*e^[(x-a)/2]/b
So the original formula = ∫ (T-A) / 2 * e ^ [(T-A) / 2] / BDT
=(2/b)∫(t-a)/2*e^[(t-a)/2]d[(t-a)/2]
=(2/b)∫(t-a)/2de^[(t-a)/2]
=(2/b)(t-a)/2*e^[(t-a)/2]-(2/b)∫e^(t-a)/2d[(t-a)/2]
=(t-a)*e^[(t-a)/2]/b-(2/b)*e^(t-a)/2
Substituting integral limit
The original formula = (Y-A) * e ^ [(Y-A) / 2] / B - (2 / b) * e ^ (Y-A) / 2-2 * e ^ B + (2 / b) * e ^ B