It's the integration of k(1+x)^-4 from 0 to infinity which is equal to 1. Solve for k.

My solution is ---

Let u=1+x du=dx

Then, it's k(-3(1+x)^-3) from 0 to infinity, which means k=1/3

But the solution manual says it's

(-k/3)(1/(1+3)^3) from 0 to infinity giving k=3

I'm not sure why it's -k/3 and not -3k

I thought when integration u^-4 it becomes -3u^-3