Evaluate the integral by making the given substitution. (Use C for the constant of integration.)

Question

∫ dt/(1-7)^7, u=1-7t

Answer 1

I suspect you mean

∫ dt/(1-7t)^7, u=1-7t

so if u = 1-7t
then du = -7 dt
or dt = -du/7

so we have
∫( -du/7)/u^7
or
-(1/7) ∫ u^-7 du

-(1/7)(-1/6) u^-6

(1/42) u^-6 + C
1/[42(1-7t)^6] + C