Question

How do you integrate ${\left(2x-5\right)}^{2}dx?$

Answer 1

We have,

$I=\int (2x-5{)}^{2}dx$

Let

$t=\left(2x-5\right)$

$dt=2dx$

So$,$ $\int {\left(2x-5\right)}^{2}dx=\frac{1}{2}\int t^{2}dt=\frac{t^3}{3}+C$

$I=\frac{{\left(2x-5\right)}^2}{6}+C$

Hence, this is the answer.