Question

integral 3x + 1 squared dx

Answer 1

you can do this by expanding and integrating term by term

(3 x + 1)^2 = 9x^2 + 6x + 1
then use the standard algebraic tntegratio

INT a x^n dx = a x^(n+1)
-------
n + 1

and then add the constant of integration C

Answer 2

You can also use a substitution approach, letting \(u=3x+1\), then \(\dfrac{1}{3}du=dx\), so
\[\int(3x+1)^2~dx=\frac{1}{3}\int u^2~du\]