Question

Integrate from 1 to 5 of (3x-5)^5 dx = Integrate from a to b of f(u) du

where (I have solved this part)
u = 3x-5
du = 3
a = 0
b = 12
The original value of the integral is 165888 via calculator

here's my last question, and it has to be in terms of u:
f(u) = ? (Again, in terms of u)

I originally thought it was 5(u)^4, then tried u^5, but to no avail. What am I doing wrong?

Answer 1

Nevermind, found the answer. It is (1/3)(u^5).

Answer 2

u = 3x-5, so
du = 3 dx, not just 3

∫[1,5] (3x-5)^5 dx = 55552

Now, subbing in for u, the limits of integration are not 0-12. Rather, we have

1/3 ∫[-2,10] u^5 du = 55552

Where did you get 165888?