Question

Evaluate the integral by making the given substitutionhttp://www.webassign.net/cgi-bin/symimage.cgi?expr=int%20%28dt%29%2F%281%20-%207%20t%29%2A%2A%287%29%20text%28%2C%20%29%20u%20%3D%201%20-%207%20t

Answer 1

\[I = \int\frac{1}{(1-7t)^7}dt\]\[u = 1-7t \Rightarrow du = -7dt \Rightarrow dt = -\frac{1}{7}du\]\[I = \int\frac{1}{u^7}\cdot-\frac{1}{7}dt = -\frac{1}{7}\int\frac{1}{u^7} = -\frac{1}{7}\frac{1}{(-6)u^6} + K = \frac{1}{42\left(1-7t\right)^6}+ K.\]