Question

Help with question (k)

Answer 1

you can directly post the question :)

Answer 2

@hartnn

Answer 3

please try the substitution:
4x-5= t, where t is the new variable of integration

Answer 4

\[\int \frac{dx}{2(4x-5)^3}=\int \frac {(4x-5)^{-3}dx}{2}\]
Let 4x-5 = t
4 dx = dt
dx = dt/4
\[\frac 1 2\int t^{-3} \frac {dt} 4 = \frac 18 \frac{t^{(-3+1)}}{-3+1} +C = \frac{t^{-2}}{-16} +C = \frac {-1}{16 t^2} +C = \frac{-1}{16 (4x-5)^2} +C\]