I want to find $\int (f'(x))^2 dx$ and $\int (f''(x))^2 dx$
I tried with the first one.
I believed that $\int (f'(x))^2 dx= f(x)+c\;$
for if I put $u=f(x)$ then $du=f'(x)dx$ I get
$$\int (f'(x))^2 dx= \int u'du=u+c=f(x)+c$$
Surely there must be something wrong here. What is it?.
Then how do I solve $\int (f'(x))^2 dx$ or $\int (f''(x))^2 dx$?